On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

Reynolds-stress turbulence model in the KIVA code for engine simulation

A Reynolds-Stress Turbulence Model has been incorporated with success into the KIVA code, a computational fluid dynamics hydrocode for three-dimensional simulation of fluid flow in engines. The newly implemented Reynolds-stress turbulence model greatly improves the robustness of KIVA, which in its original version has only eddy-viscosity turbulence models. Validation of the Reynolds-stress turbulence model is accomplished by conducting pipe-flow and channel-flow simulations, and comparing the computed results with experimental and direct numerical simulation data. Flows in engines of various geometry and operating conditions are calculated using the model, to study the complex flow fields as well as confirm the model’s validity. Results show that the Reynolds-stress turbulence model is able to resolve flow details such as swirl and recirculation bubbles. The model is proven to be an appropriate choice for engine simulations, with consistency and robustness, while requiring relatively low computational effort.

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.

Critical evaluation of diameter increment modelling in the Great Lakes region

Simulations of forest stand dynamics in a modelling framework including Forest Vegetation Simulator (FVS) are diameter driven, thus the diameter or basal area increment model needs a special attention. This dissertation critically evaluates diameter or basal area increment models and modelling approaches in the context of the Great Lakes region of the United States and Canada. A set of related studies are presented that critically evaluate the sub-model for change in individual tree basal diameter used in the Forest Vegetation Simulator (FVS), a dominant forestry model in the Great Lakes region. Various historical implementations of the STEMS (Stand and Tree Evaluation and Modeling System) family of diameter increment models, including the current public release of the Lake States variant of FVS (LS-FVS), were tested for the 30 most common tree species using data from the Michigan Forest Inventory and Analysis (FIA) program. The results showed that current public release of the LS-FVS diameter increment model over-predicts 10-year diameter increment by 17% on average. Also the study affirms that a simple adjustment factor as a function of a single predictor, dbh (diameter at breast height) used in the past versions, provides an inadequate correction of model prediction bias. In order to re-engineer the basal diameter increment model, the historical, conceptual and philosophical differences among the individual tree increment model families and their modelling approaches were analyzed and discussed. Two underlying conceptual approaches toward diameter or basal area increment modelling have been often used: the potential-modifier (POTMOD) and composite (COMP) approaches, which are exemplified by the STEMS/TWIGS and Prognosis models, respectively. It is argued that both approaches essentially use a similar base function and neither is conceptually different from a biological perspective, even though they look different in their model forms. No matter what modelling approach is used, the base function is the foundation of an increment model. Two base functions – gamma and Box-Lucas – were identified as candidate base functions for forestry applications. The results of a comparative analysis of empirical fits showed that quality of fit is essentially similar, and both are sufficiently detailed and flexible for forestry applications. The choice of either base function in order to model diameter or basal area increment is dependent upon personal preference; however, the gamma base function may be preferred over the Box-Lucas, as it fits the periodic increment data in both a linear and nonlinear composite model form. Finally, the utility of site index as a predictor variable has been criticized, as it has been widely used in models for complex, mixed species forest stands though not well suited for this purpose. An alternative to site index in an increment model was explored, using site index and a combination of climate variables and Forest Ecosystem Classification (FEC) ecosites and data from the Province of Ontario, Canada. The results showed that a combination of climate and FEC ecosites variables can replace site index in the diameter increment model.

Reverse Engineering the Structural and Acoustic Behavior of a Stradivari Violin

There is a tremendous amount of mystery that surrounds the instruments of Antonio Stradivari. There have been many studies done in the past, but no one completely understands exactly how he made his instruments, or why they are still considered the best in the world. This project is designed to develop an engineering model of one of Stradivari's violins that will accurately simulate the structural and acoustic behavior of the instrument. It also hopes to shine some light on what makes the instruments of Stradivari unique when compared to other violins. It will focus on geometry and material properties, utilizing several modern engineering tools, including CT scanning, experimental modal analysis, finite element analysis, correlation techniques, and acoustic synthesis.

Two-Phase Flow In Microchannels: Morphology And Interface Phenomena

The existence and morphology, as well as the dynamics of micro-scale gas-liquid interfaces is investigated numerically and experimentally. These studies can be used to assess liquid management issues in microsystems such as PEMFC gas flow channels, and are meant to open new research perspectives in two-phase flow, particularly in film deposition on non-wetting surfaces. For example the critical plug volume data can be used to deliver desired length plugs, or to determine the plug formation frequency. The dynamics of gas-liquid interfaces, of interest for applications involving small passages (e.g. heat exchangers, phase separators and filtration systems), was investigated using high-speed microscopy - a method that also proved useful for the study of film deposition processes. The existence limit for a liquid plug forming in a mixed wetting channel is determined by numerical simulations using Surface Evolver. The plug model simulate actual conditions in the gas flow channels of PEM fuel cells, the wetting of the gas diffusion layer (GDL) side of the channel being different from the wetting of the bipolar plate walls. The minimum plug volume, denoted as critical volume is computed for a series of GDL and bipolar plate wetting properties. Critical volume data is meant to assist in the water management of PEMFC, when corroborated with experimental data. The effect of cross section geometry is assessed by computing the critical volume in square and trapezoidal channels. Droplet simulations show that water can be passively removed from the GDL surface towards the bipolar plate if we take advantage on differing wetting properties between the two surfaces, to possibly avoid the gas transport blockage through the GDL. High speed microscopy was employed in two-phase and film deposition experiments with water in round and square capillary tubes. Periodic interface destabilization was observed and the existence of compression waves in the gas phase is discussed by taking into consideration a naturally occurring convergent-divergent nozzle formed by the flowing liquid phase. The effect of channel geometry and wetting properties was investigated through two-phase water-air flow in square and round microchannels, having three static contact angles of 20, 80 and 105 degrees. Four different flow regimes are observed for a fixed flow rate, this being thought to be caused by the wetting behavior of liquid flowing in the corners as well as the liquid film stability. Film deposition experiments in wetting and non-wetting round microchannels show that a thicker film is deposited for wetting conditions departing from the ideal 0 degrees contact angle. A film thickness dependence with the contact angle theta as well as the Capillary number, in the form h_R ~ Ca^(2/3)/ cos(theta) is inferred from scaling arguments, for contact angles smaller than 36 degrees. Non-wetting film deposition experiments reveal that a film significantly thicker than the wetting Bretherton film is deposited. A hydraulic jump occurs if critical conditions are met, as given by a proposed nondimensional parameter similar to the Froude number. Film thickness correlations are also found by matching the measured and the proposed velocity derived in the shock theory. The surface wetting as well as the presence of the shock cause morphological changes in the Taylor bubble flow.

ModelDB in Computational Neuroscience Education - A research tool as interactive educational media

ModelDB's mission is to link computational models and publications, supporting the field of computational neuroscience (CNS) by making model source code readily available. It is continually expanding, and currently contains source code for more than 300 models that cover more than 41 topics. Investigators, educators, and students can use it to obtain working models that reproduce published results and can be modified to test for new domains of applicability. Users can browse ModelDB to survey the field of computational neuroscience, or pursue more focused explorations of specific topics. Here we describe tutorials and initial experiences with ModelDB as an interactive educational tool.

GPU-based Ray Tracing of Dynamic Scenes

Interactive ray tracing of non-trivial scenes is just becoming feasible on single graphics processing units (GPU). Recent work in this area focuses on building effective acceleration structures, which work well under the constraints of current GPUs. Most approaches are targeted at static scenes and only allow navigation in the virtual scene. So far support for dynamic scenes has not been considered for GPU implementations. We have developed a GPU-based ray tracing system for dynamic scenes consisting of a set of individual objects. Each object may independently move around, but its geometry and topology are static.

Ragu: a free tool for the analysis of EEG and MEG event-related scalp field data using global randomization statistics

We present a program (Ragu; Randomization Graphical User interface) for statistical analyses of multichannel event-related EEG and MEG experiments. Based on measures of scalp field differences including all sensors, and using powerful, assumption-free randomization statistics, the program yields robust, physiologically meaningful conclusions based on the entire, untransformed, and unbiased set of measurements. Ragu accommodates up to two within-subject factors and one between-subject factor with multiple levels each. Significance is computed as function of time and can be controlled for type II errors with overall analyses. Results are displayed in an intuitive visual interface that allows further exploration of the findings. A sample analysis of an ERP experiment illustrates the different possibilities offered by Ragu. The aim of Ragu is to maximize statistical power while minimizing the need for a-priori choices of models and parameters (like inverse models or sensors of interest) that interact with and bias statistics.

Ontologies and Methods for Interoperability of Engineering Analysis Models (EAMS) in an E-Design Environment

ABSTRACT ONTOLOGIES AND METHODS FOR INTEROPERABILITY OF ENGINEERING ANALYSIS MODELS (EAMS) IN AN E-DESIGN ENVIRONMENT SEPTEMBER 2007 NEELIMA KANURI, B.S., BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCES PILANI INDIA M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Ian Grosse Interoperability is the ability of two or more systems to exchange and reuse information efficiently. This thesis presents new techniques for interoperating engineering tools using ontologies as the basis for representing, visualizing, reasoning about, and securely exchanging abstract engineering knowledge between software systems. The specific engineering domain that is the primary focus of this report is the modeling knowledge associated with the development of engineering analysis models (EAMs). This abstract modeling knowledge has been used to support integration of analysis and optimization tools in iSIGHT FD , a commercial engineering environment. ANSYS , a commercial FEA tool, has been wrapped as an analysis service available inside of iSIGHT-FD. Engineering analysis modeling (EAM) ontology has been developed and instantiated to form a knowledge base for representing analysis modeling knowledge. The instances of the knowledge base are the analysis models of real world applications. To illustrate how abstract modeling knowledge can be exploited for useful purposes, a cantilever I-Beam design optimization problem has been used as a test bed proof-of-concept application. Two distinct finite element models of the I-beam are available to analyze a given beam design- a beam-element finite element model with potentially lower accuracy but significantly reduced computational costs and a high fidelity, high cost, shell-element finite element model. The goal is to obtain an optimized I-beam design at minimum computational expense. An intelligent KB tool was developed and implemented in FiPER . This tool reasons about the modeling knowledge to intelligently shift between the beam and the shell element models during an optimization process to select the best analysis model for a given optimization design state. In addition to improved interoperability and design optimization, methods are developed and presented that demonstrate the ability to operate on ontological knowledge bases to perform important engineering tasks. One such method is the automatic technical report generation method which converts the modeling knowledge associated with an analysis model to a flat technical report. The second method is a secure knowledge sharing method which allocates permissions to portions of knowledge to control knowledge access and sharing. Both the methods acting together enable recipient specific fine grain controlled knowledge viewing and sharing in an engineering workflow integration environment, such as iSIGHT-FD. These methods together play a very efficient role in reducing the large scale inefficiencies existing in current product design and development cycles due to poor knowledge sharing and reuse between people and software engineering tools. This work is a significant advance in both understanding and application of integration of knowledge in a distributed engineering design framework.

Effect of lateral meniscectomy and osteochondral grafting of a lateral femoral condylar defect on contact mechanics: a cadaveric study in dogs

BACKGROUND Osteochondral autograft transfer (OAT) aims at restoring normal articular cartilage surface geometry and articular contact mechanics. To date, no studies have evaluated the contact mechanics of the canine stifle following OAT. Additionally, there are no studies that evaluated the role of the meniscus in contact mechanics following OAT in human or canine femorotibial joints. The objective of this study was to measure the changes in femorotibial contact areas (CA), mean contact pressure (MCP) and peak contact pressure (PCP) before and after osteochondral autograft transplantation (OAT) of a simulated lateral femoral condylar cartilage defect with an intact lateral meniscus and following lateral meniscectomy. RESULTS With an intact lateral meniscus, creation of an osteochondral defect caused a decrease in MCP and PCP by 11% and 30%, respectively, compared to the intact stifle (p < 0.01). With an intact meniscus, implanting an osteochondral graft restored MCP and PCP to 96% (p = 0.56) and 92% (p = 0.41) of the control values. Lateral meniscectomy with grafting decreased CA by 54% and increased PCP by 79% compared to the intact stifle (p < 0.01). CONCLUSIONS OAT restored contact pressures in stifles with a simulated lateral condylar defect when the meniscus was intact. The lateral meniscus has a significant role in maintaining normal contact pressures in both stifles with a defect or following OAT. Meniscectomy should be avoided when a femoral condylar defect is present and when performing OAT.

Two-dimensional supramolecular polymers: controlled formation and visualization on the surface

Self – assembly is a powerful tool for the construction of highly organized nanostructures. Therefore, the possibility to control and predict pathways of molecular ordering on the nanoscale level is a critical issue for the production of materials with tunable and adaptive macroscopic properties. 2D polymers are attractive objects for the field of material sciences due to their exceptional properties. [1] As shown before, amphiphilic oligopyrenotides (produced via automated solid-phase synthesis) form rod–like supramolecular polymers in water. [2] These assemblies form 1D objects. [3] By applying certain changes to the design of the oligopyrenotide units the dimensionality of the formed assemblies can be influenced. Herein, we demonstrate that Py3 (see Figure 1) forms defined supramolecular assemblies under thermodynamic conditions in water. To study Py3 self-assembly, we carried out whole set of spectroscopic (UV/vis, fluorescence, DLS) and microscopic experiments (AFM). The obtained results suggest that oligopyrenotides with the present type of geometry and linker length leads to formation of 2D supramolecular assemblies.

Cortical remodeling during menopause, rheumatoid arthritis, glucocorticoid and bisphosphonate therapy

Bone mass, bone geometry and its changes are based on trabecular and cortical bone remodeling. Whereas the effects of estrogen loss, rheumatoid arthritis (RA), glucocorticoid (GC) and bisphosphonate (BP) on trabecular bone remodeling have been well described, the effects of these conditions on the cortical bone geometry are less known. The present review will report current knowledge on the effects of RA, GC and BP on cortical bone geometry and its clinical relevance. Estrogen deficiency, RA and systemic GC lead to enhanced endosteal bone resorption. While in estrogen deficiency and under GC therapy endosteal resorption is insufficiently compensated by periosteal apposition, RA is associated with some periosteal bone apposition resulting in a maintained load-bearing capacity and stiffness. In contrast, BP treatment leads to filling of endosteal bone cavities at the epiphysis; however, periosteal apposition at the bone shaft seems to be suppressed. In summary, estrogen loss, RA and GC show similar effects on endosteal bone remodeling with an increase in bone resorption, whereas their effect on periosteal bone remodeling may differ. Despite over 50 years of GC therapy and over 25 years of PB therapy, there is still need for better understanding of the skeletal effects of these drugs as well as of inflammatory disease such as RA on cortical bone remodeling.