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Title: SITE-DIRECTED MUTAGENESIS STUDY OF VITREOSCILLA HEMOGLOBIN-THE ROLE OF TYROSINE (B10) AND PROLINE (E8) IN THE STRUCTURE OF THE LIGAND-BINDING SITE
Creator: Zhang, Yifan
Date: 2015, 2015-05
Description: Vitreoscilla is a genus of Gram-negative aerobic bacterium which has the capability to synthesis a soluble, homodimertic hemoglobin,...
Show moreVitreoscilla is a genus of Gram-negative aerobic bacterium which has the capability to synthesis a soluble, homodimertic hemoglobin, Vitreoscilla hemoglobin (VHb). The Vitreoscilla hemoglobin was the first bacterial hemoglobin discovered, and has a wide range of biological and biotechnological applications. The distal site is one of the hot spots in VHb studies because of its unique structure. The Tyrosine residue at B10 and its hydrogen bonded Proline at E8 were considered as the ligand binding functional sites in distal space of VHb according to the previous study. In this study, two single mutated and one double mutated Vitreoscilla hemoglobin at position B10 and E8 were constructed and purified. In the two single mutants, the Tyr at B10 and the Pro at E8 were mutated to Ala. In the double mutant, both of the sites were mutated to Ala. The CO di↵erence spectrum data of the mutants indicate that the ligand binding ability of the Vitreoscilla hemoglobin was not neutralized by the mutations at ProE8 and TyrB10. Circular dichroism spectrum data of the mutants is similar to the wild type Vitreoscilla hemoglobin, which means the globin secondary structure is conserved. However the micro-environment in the distal sites is changed: the IR spectrum of the carbonyl stretch bond red-shifted in the CO bound VHb double mutant. A molecular dynamic simulation was introduced in the study to o↵er some guidance for future research plans. The simulation results showed that the B10 and E8 residue mutated to Ala might reduce the flexibility of the D-region, because of the more completed C and E helix. The volume of cavity where the heme group inserts changes significantly in various mutant models, which may provide a rough explanation of the change in carbonyl stretch bond IR spectrum. Additionally, an interesting conformation of Gln E7 was found in the simulation of double mutant model.
M.S. in Biology, May 2015
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Title: DISTRIBUTED VIDEO CODING FOR RESOURCE CONSTRAINED VIDEO APPLICATIONS
Creator: Liu, Wenhui
Date: 2014, 2014-05
Description: Video coding technology has played a key role in the explosion of current multimedia society with increasing resolution and quality. Such big...
Show moreVideo coding technology has played a key role in the explosion of current multimedia society with increasing resolution and quality. Such big success is largely built on the conventional video coding paradigm where motion estimation and compensation are performed at the encoder. This asymmetry in complexity is well-suited for the applications where the video sequence is encoded once and decoded many times. However, some new emerging applications such as wireless video surveillance, wireless PC cameras and multimedia sensor networks require a low complexity encoding, while possibly a ording a high complexity decoding. Therefore, a challenging problem emerges with the new type of visual communication system is how to achieve low complexity encoding video compression while maintaining good coding e ciency. Distributed video coding (DVC) provides low complexity encoding solutions for video communication with limited computational power or energy constraints. In DVC, the source video information is independently encoded at lightweight encoders. At the decoder, all the received bitstreams are jointly exploited their statistical dependencies between them. In such a way, motion estimation and its computational complexity is shifted from the encoder to the decoder. However, DVC also has its own restrictions. The low coding e ciency remains a challenging issue for DVC compare to the conventional video coding. Although DVC is robust to channel loss due to its intrinsic feature of independent encoders and joint decoder, the error resiliency for medium to large transmission errors is weak. In this dissertation, previously proposed low-complexity DVC (LC-DVC) architecture is rstly introduced. After that, a continued work is presented to further improve quality of SI. The proposed method is called spatio-temporal joint bilateral upsampling (STJBU) based SI generation, where geometric closeness of pixels and their photometric similarity is exploited to reduce the noise while preserving the edge xiv information. Moreover, a distributed multiple description coding (DMDC) scheme is proposed by combining the multiple description (MD) coding into LC-DVC to improve its error resiliency. All the proposed schemes are well described and the ratedistortion analyses are presented in this dissertation. All these features have made the LC-DVC a great solution for resource constraints applications.
PH.D in Electrical Engineering, May 2014
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Title: MIN- AREA RETIMING UNDER WIRE-DELAY MODEL
Creator: Luo, Tianchen
Date: 2011-05-09, 2011-05
Description: Retiming is a powerful optimization technique for synchronize sequential circuits that relocates delay unit without changing the circuit’s...
Show moreRetiming is a powerful optimization technique for synchronize sequential circuits that relocates delay unit without changing the circuit’s input-output functionality. Wire delay is significant and can no longer be ignored in deep sub-micrometer technologies. Existing algorithms solve the problem of min-area and min-period either optimal or heuristically without taking wire delay into consideration. However, those techniques cannot be applied directly to circuit with wire delay. Recent work solved the min-period problem under wire delay model. This paper proposes an algorithm that solves the problem of min-area wire retiming under fixed clock period optimally and efficiently.
M.S. in Electrical and Computer Engineering, May 2011
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Title: Nonlinear time series models for multivariable dynamic processes
Creator: Cinar, A.
Date: 1995-11
Publisher: ELSEVIER SCIENCE BV
Description: Several paradigms are available for developing nonlinear dynamic input-output models of processes. Polynomial models, threshold models, models...
Show moreSeveral paradigms are available for developing nonlinear dynamic input-output models of processes. Polynomial models, threshold models, models based on spline functions, and polynomial models with exponential and trigonometric functions can describe various types of nonlinearities and pathological behavior observed in many physical processes. A unified nonlinear model development framework is not available, and the search of the appropriate nonlinear structure is part of the model development effort. Various artificial neural network structures and nonlinear time series model structures are presented and illustrated by developing a model from data sets generated by a series of example systems. The use of a nonlinear model development paradigm which is not compatible with the types of nonlinearities that exist in the data can have a significant effect on model development effort and model accuracy.
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Title: INCORPORATING INVARIANCE INTO SUPPORT VECTOR MACHINE FOR DETECTION OF MICROCALCIFICATIONS
Creator: Yang, Yan
Date: 2011-11-16, 2011-12
Description: In this thesis, we explore methods for incorporating invariance into a support vector machine (SVM) classifier in detection of clustered...
Show moreIn this thesis, we explore methods for incorporating invariance into a support vector machine (SVM) classifier in detection of clustered microcalcifications (MC) in mammogram images. Unlike standard SVM, both virtual SVM and tangent vector SVM can include prior information into a trained model. We formulate MC detection as a two-class classification problem and apply these three types of SVM classifiers to this problem. The issue of dimensional reduction is considered in the tangent vector SVM, which has influence on the computational cost and complexity of the algorithm. We test and compare their performance on a set of 200 clinical mammogram images which contain a total of 5,115 MCs. In the experiments these classifiers are optimized with a training procedure for model selection. We evaluate the detection performance using both receiver operating characteristic (ROC) curves and free-response operating characteristic (FROC) curves. The results show that both virtual SVM and tangent vector SVM can outperform the standard SVM. The use of dimensional reduction in tangent vector SVM can effectively reduce the computational cost.
M.S. in Electrical Engineering, December 2011
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Title: MATHEMATICAL-MODELS OF COCURRENT SPRAY-DRYING
Creator: Negiz, A., Lagergren, E. S., Cinar, A.
Date: 1995-10
Publisher: AMER CHEMICAL SOC
Description: A steady state mathematical model for a cocurrent spray dryer-is developed. The model includes the mass, momentum, and energy balances for a...
Show moreA steady state mathematical model for a cocurrent spray dryer-is developed. The model includes the mass, momentum, and energy balances for a single drying droplet as well as the total energy and mass balances of the drying medium. A log normal droplet size distribution is assumed to hold at the exit of the twin-fluid atomizer located at the top of the drying chamber. The discretization of this log normal distribution with a certain number of bins yields a system of nonlinear coupled first-order differential equations as a function of the axial distance of the drying chamber. This system of equations is used to compute the axial changes in droplet diameter, density, velocity, moisture, and temperature for the droplets at each representative bin. Furthermore, the distributions of important process parameters such as droplet moisture content, diameter, density, and temperature are also obtainable along the length of the chamber. On the basis of the developed model, a constrained nonlinear optimization problem is solved, where the exit particle moisture content is minimized with respect to the process inputs subjected to a fixed mean particle diameter at the chamber exit. Response surface studies based on empirical models are also performed to illustrate the effectiveness of these techniques in achieving the optimal solution when an a priori model is not available. The structure of empirical models obtained from the model is shown to be in agreement with the structure of the empirical models obtained from the experimental studies.
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Title: Tests on the gravity cell
Creator: Evans, P. W., Linderberg, W. A.
Date: 2009, 1912
Publisher: Armour Institute of Technology
Description: http://www.archive.org/details/testsongravityce00evan
Thesis (B.S.)--Armour Institute of Technology

Title: Planning for Human Implantation of a Cortical Visual Prosthesis (sequence unknown), IPRO 334 - Deliverables: IPRO 334 Final Report F09
Creator: Bern, David, Chen, Shanyl, Deroo, Mary, Gorski, David, Kelly, Thomas, Leasenby, Alex, Li, Zhi, Pyrkh, Hanna, Subhani, Maham, Taneja, Aanchal
Date: 2009-12
Description: The Intracortical Visual Prosthesis is based upon that concept that by implanting a large number of subminiature electrodes within the human...
Show moreThe Intracortical Visual Prosthesis is based upon that concept that by implanting a large number of subminiature electrodes within the human visual cortex, coordinated temporal-spatial image information can be artificially communicated to the human visual cortex in the form of electrical currents, acting as a sensory substitute for normal vision.
Sponsorship: IIT Laboratory of Neural Prosthetic Research
Deliverables for IPRO 334: Planning for Human Implantation of a Cortical Visual Prosthesis for the fall 2009 semester
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Title: ECONOMIC BASED CONTROL SYSTEM DESIGN
Creator: Omell, Benjamin Peter
Date: 2013, 2013-12
Description: EMPC differs from traditional MPC by directly utilizing a profit based function as the objective as opposed to a quadratic function that...
Show moreEMPC differs from traditional MPC by directly utilizing a profit based function as the objective as opposed to a quadratic function that minimizes the distance from a set point that is predetermined. However, implementation of EMPC can result in unexpected and at times pathological closed-loop behavior, including inventory creep, bang-bang actuation and instability. To address these issues, an infinite-horizon version of EMPC is developed and shown to avoid many of the performance issues observed in the finite-horizon version. First, modifications to the EMPC problem will be used for the conceptual development of the Economic Linear Optimal Controller (ELOC), which is a statistically constrained linear feedback controller. Then, pointwise- in-time constraints can be reintroduced using one of two methods; Constrained ELOC or Infinite-Horizon EMPC (IH-EMPC). We also investigate the impact of problem formulation modifications on the ELOC. The first issue is that of disturbance modeling and the second is the impact of controller sample-time. The third topic concerns incorporation of computational delay in the feedback-loop, using both full and partial state information structures. Finally an illustration of the impact of plant-model mismatch is presented. The Constrained ELOC formulation is further modified to allow for market responsive smart grid applications. In particular an Integrated Gasification Combined Cycle (IGCC) process with hydrogen storage will be used to demonstrate the Constrained ELOC for such applications. The ELOC will be used as a vehicle to exploit dispatch capabilities by pursuing directly the objective of maximizing revenue. The idea being that process modifications to enable dispatch capabilities will allow for a time-shift of power production away from periods of low energy value to periods of high value. An in depth discussion is provided on how energy value forecasts are incorporated into the design of the constrained ELOC. Finally, an extension of the ix ELOC to the controller embedded equipment design is provided. The work concludes with a discussion of the computational aspects of solving the ELOC problem. In particular, the impact of reverse-convex constraints inherent to the ELOC problem are discussed along with existing solution methods. The main contribution of this final chapter is a novel application of the Generalized Bender’s Decomposition (GBD) algorithm to the ELOC problem. This new approach is shown to retain global optimality, reduce computational effort (by orders of magnitude) and expand the class of problems one can solve.
PH.D in Chemical Engineering, December 2013
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Title: POWER OPTIMIZATION IN DEEP SUBMICRON VLSI CIRCUITS: FROM SYSTEM LEVEL TO CIRCUIT LEVEL
Creator: Tong, Qiang
Date: 2017, 2017-07
Description: As VLSI technology advances to deep sub-micron regime, power consumption has become a critical concern in VLSI circuits. Therefore, power...
Show moreAs VLSI technology advances to deep sub-micron regime, power consumption has become a critical concern in VLSI circuits. Therefore, power optimization becomes mandatory in VLSI design nowadays. To reduce the power consumption, many techniques have been proposed at various levels of VLSI circuits design: system level, register-transfer level(RTL), and circuit/transistor level. This dissertation starts with a review of system level power optimization techniques. Experiments on a computer architecture simulation system have been conducted to compare the impact of different programming styles at system level on power consumption. The results could be used as an intuitive guidance for programmers with intention for implementing power-aware system. The second topic in this dissertation is a clustering based clock gating technique, targeting power reduction at RT-Level. Clock gating is an effective and popular method to reduce dynamic power in VLSI circuits, it can be applied at both RT-level and gate level. The basic idea of clock gating is to disable the clock of one or more sequential logics (majorly flip-flops) when the input data of the logic cells do not change. In this dissertation, a clustering based clock gating technique is proposed, the technique exploits activity information of each flip-flop, and clusters them into groups according to their activity correlations. As the leakage power has become a major concern in VLSI design, the proposed As the leakage power has become a major concern in VLSI design, the proposed clustering method is extended down to gate level and a clustering based hybrid clock gating and power gating technique is proposed. The technique can reduce both the dynamic power and leakage power in VLSI circuits. As process technology scaling down to deep submicron regime, bulk CMOS technology has encountered many challenges due to short channel effect (SCE), which degrades the reliability and feasibility of MOSFET devices. New technologies such as FinFET and carbon nanotube FET (CNFET) are two promising substitute solutions in the following decade to address SCE issue. Part of this dissertation presents circuit design using these new process technologies for low power VLSI circuits. More specifically, two SRAM cell designs using FinFET and CNFET devices are proposed. The new designs can improve performance while reduce power consumption.
Ph.D. in Electrical Engineering, July 2017
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Title: Devices that Assist Blind & Visually-Impaired Individuals in Swimming and Other Exercise Activities (sequence unknown), IPRO 310 - Deliverables
Creator: Dykeman, Kimberly, Healton, Michaela, Lipman, Timothy, Ludwig, Ross, Park, Jay, Reilly, Jeffrey, Sarkar, Smita, Sirk, Phillip, Toro, Branden
Date: 2009-12
Description: The objective is to develop, test, and implement assistive technology with the community that promotes safety and improves independence of...
Show moreThe objective is to develop, test, and implement assistive technology with the community that promotes safety and improves independence of blind and visually impaired (BVI) swimmers.
Sponsorship: Chicago Lighthouse for the Blind & Visually-Impaired. Notre Dame University
Deliverables for IPRO 310:Devices that Assist Blind & Visually-Impaired Individuals in Swimming and Other Exercise Activities for the fall 2009 semester.
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Title: NATURAL AGING EFFECT ON DOUBLE AGED ALUMINUM ALLOY AA7075
Creator: Kara, Baris
Date: 2012-04-27, 2012-05
Description: The effect of natural aging (NA) on mechanical properties in double aged aluminum alloys, AA7075, was studied by means of hardness tests,...
Show moreThe effect of natural aging (NA) on mechanical properties in double aged aluminum alloys, AA7075, was studied by means of hardness tests, tensile tests and stress corrosion cracking (SCC) tests. Natural aging can strengthen AA7075 alloys after solution heat treatment, and reaching the stable condition can take years for the alloy. Double aging (DA) is very beneficial method in terms of energy savings and productivity because this method provides the peak hardness in a much shorter time compared to single aging, and DA treatment produces hardness, yield stress and tensile stress which are comparable with those produced by SA. In this study, the alloys were naturally aged for different times before double aging treatment, and the relationship between double aging treatment and natural aging treatment was observed. The results show that different natural aging times do not significantly affect the final mechanical properties of double aged alloys. Consequently, the loading time to aging furnace after solution heat treatment does not play an important role in the double aging treatment of AA7075 alloys.
M.S. in Materials Science and Engineering, May 2012
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Title: Using Assessment Data to Improve Library Services : presented at ILA 2007 conference
Creator: Stewart, Christopher, Uth, Charles
Date: 2007-10
Description: IIT Libraries conducted LibQUAL+ service quality assessment in 2004 and 2006. This presentation will outline strategies we undertook to...
Show moreIIT Libraries conducted LibQUAL+ service quality assessment in 2004 and 2006. This presentation will outline strategies we undertook to address issues identified in the 2004 assessment, and evaluate their success based on assessment results in 2006. We will also discuss the importance of measuring academic library effectiveness in higher education’s emerging outcomes-based culture.
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Title: High Performance Green Homes (sequence unknown), IPRO 317 - Deliverables: IPRO 317 Midterm Presentation F09
Creator: Bhat, Adnan, Campbell, Brittanie, Cink, Jefferey, Gutstein, Yehuda, Hadi, Shuaib, Hafdi, Kamal, Hasan, Hasan, Kenig, Elezar, Lipski, Brian, Lollino, Luca, Margolis, Jordan, Nigamatzyanov, Tagir, Patel, Hiren, Patel, Neal, Shehada, Hazem, Toops, Melissa, Trauner, Crystal, Zgourdah, Mourad
Date: 2009-12
Description: The purpose of this project is to show how a team committed to helping people help save the world can leapfrog today's best designs. As...
Show moreThe purpose of this project is to show how a team committed to helping people help save the world can leapfrog today's best designs. As opposed to the tradition of minimum design standards that just meeting the building code, highest practical design standards are the focus. True sustainability is the goal of this project, including; Zero Carbon Emissions, Net Zero Energy, 100% Solar Power, 10 times the traditional design life, 1/10th the maintenance, rot proof, termite proof, fire proof, hurricane and earthquake resistant. The project team, using cutting edge technology, will develop all aspects of a start-up design and build company to promote High Performance Green Homes. This project will provide a great opportunity for IIT students to experience a challenging and interesting project and to significantly contribute to a better world.
Sponsorship: Jimmy Eng
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Title: FLEXIBLE COGNITIVE STYLE MODERATES THE RELATIONSHIP BETWEEN RUMINATION AND AFFECT
Creator: Smetter, Joseph B.
Date: 2014, 2014-12
Description: Prospective and longitudinal studies have demonstrated that rumination has a negative effect on mood and depression outcomes. The present...
Show moreProspective and longitudinal studies have demonstrated that rumination has a negative effect on mood and depression outcomes. The present study examined whether the type of flexible cognitive style needed to reevaluate maladaptive thoughts and interpretations (i.e. cognitive flexibility) acts as a buffer against the negative relationship between rumination and affect. Participants (N = 100) completed anonymous online surveys containing two measures of cognitive flexibility, including the Beck Cognitive Insight Scale (BCIS; Beck et al., 2008) and the Cognitive Flexibility Inventory (CFI; Dennis & Vander Wal, 2010), as well as measures of depressive rumination and trait affect. Multiple regression-based moderation analyses showed that the tendency to be more objective, reflective, and open to feedback moderated the relationship between rumination and positive affect (PA), such that the negative relationship between rumination and PA was attenuated for individuals who were more self-reflective. We discuss the implications of this buffering effect for theories of rumination and research on protective factors, as well as its relevance to psychotherapy. A comparison of the cognitive flexibility questionnaires revealed differences in how flexible reinterpretation is measured and identified selective relationships to positive and negative affect. Based on these findings, we provide recommendations for future research on cognitive styles that promote flexible reinterpretation.
M.S. in Psychology, December 2014
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Title: STAR Results from the RHIC Beam Energy Scan, Proceedings of the XLIII International Symposium on Multiparticle Dynamics
Creator: Wang, Hui
Date: 2013-09-15, 2013-09-15
Publisher: IIT Press
Description: The Beam Energy Scan Program is launched by RHIC to study the QCD phase diagram. The goal is to explore the possible QCD phase boundary and...
Show moreThe Beam Energy Scan Program is launched by RHIC to study the QCD phase diagram. The goal is to explore the possible QCD phase boundary and search for possible QCD critical point. In 2010 and 2011, experiments collected data at √sNN=7.7, 11.5, 19.6, 27, 39 and 62.4 GeV, covering a wide range of baryon chemical potential from μB 420 to 70 MeV. In this presentation, we will report some latest results of the Beam Energy Scan Program from the STAR collaboration.
Sponsorship: IIT College of Science, High Energy Physics Division of Argonne National Laboratory
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Title: SYSTEM DESIGN AND HARDWARE VERIFICATION OF A S-MFCW RADAR
Creator: Nadkarni, Satwik
Date: 2014, 2014-05
Description: Low cost imaging radar systems are an emerging field today with very useful applications in automotive, healthcare and entertainment...
Show moreLow cost imaging radar systems are an emerging field today with very useful applications in automotive, healthcare and entertainment industries. The aim is to realize an effective and reliable radar system that has a good resolution and at the same time a low cost and complexity. The S-MFCW radar technique has been shown to achieve comparable resolution with the FMCW technique while at the same time maintaining the advantages of reduced hardware complexity and low power consumption. This makes the S-MFCW technique very useful in low cost and low complexity user end devices. The aim of this thesis is to develop a S-MFCW radar system that is capable of measuring distance of an object as well as its velocity. The radar system was implemented using two different approaches – a modular approach and an integrated approach. Both the implementations were tested and the results were found to be in line with expectations from previous research work.
M.S. in Electrical Engineering, May 2014
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Title: THE CORRELATION BETWEEN FATIGUE PROPERTY AND PORE MORPHOLOGY OF POWDER METALLURGY TI6AL4V
Creator: Yan, Yingjie
Date: 2012-12-12, 2012-12
Description: The microstructure and fatigue properties of sintered Ti-6Al-4V were investi- gated as a function of sintered density and pore morphology. A...
Show moreThe microstructure and fatigue properties of sintered Ti-6Al-4V were investi- gated as a function of sintered density and pore morphology. A quantitative analysis of microstructure was conducted to correlate with tensile and fatigue properties to understand the in uence of sintering density and pore morphology. Low cycle fatigue (LCF) using constant strain control was conducted at room temperature, R=-1 and sine waveform. High cycle fatigue (HCF) using constant stress control was conducted at room temperature, R=0.1 and sine waveform. It was found that there was no signi cant di erence in tensile strength but the fatigue endurance limit was increased by 20% when the sintering density was increased from 95% to 99%. Moreover, fatigue endurance limit was increased when the shape factor increased among three di er- ent sintering conditions(1010 -60min-690MPa, 1130 -90min-410MPa, 1250 -30min- 550MPa). Fracture surface analysis indicated that the fatigue crack initiated from the cluster of pore either at surface or at the sub-surface. The implication of pore morphology and porosity on mechanical behaviour and fatigue fracture of P/M Ti- 6Al-4V were discussed. It was estimated that the shape factor was 0.05 for A-50 and 0.07 for A-100, respectively. A polynomial relationship was found between the fatigue endurance limit and shape factor among three sintering con gurations. It was found that the PM parts with a higher shape factor had a higher fatigue endurance limit.
M.S. in Materials Science and Engineering, December 2012
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Title: BIOPHYSICAL AND BIOCHEMICAL STUDY OF NATIVE AND EDITED DYSTROPHIN ROD REGION
Creator: Mangat, Khushdeep
Date: 2014, 2014-12
Description: Duchenne Muscular Dystrophy (DMD) is a severe X-linked recessive disease affecting 1 in 3500 boys that is characterized by the degeneration of...
Show moreDuchenne Muscular Dystrophy (DMD) is a severe X-linked recessive disease affecting 1 in 3500 boys that is characterized by the degeneration of muscle function and strength. The cause of this disease lies in gene defects that eliminate expression of the protein dystrophin. Becker Muscular Dystrophy, BMD is a milder form of disease that has a later onset and much longer survival (up to the 7th decade of life, compared to median survival of 25 years for DMD patients) because of the presence of low levels of modified dystrophin protein. BMD is very heterogeneous, however, and many cases are nearly as severe as DMD. A major therapy for DMD involves exon skipping, which produces modified forms of dystrophin that are very similar to BMD. However, how these edits impact the function of dystrophin, and how they are linked to the severity of BMD or the BMD-like state produced in DMD exon skip therapy is unknown. We investigated this in two specific cases involving a specific panel of BMD defects linked to a major cause of death, dilated cardiomyopathy (DCM). We also investigated the contribution of various exons to interaction with a signaling partner of dystrophin, neuronal nitric oxide synthetase (nNOS).
Ph.D. in Biological and Chemical Sciences, December 2014
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Title: PHYSICS-PRESERVING FINITE DIFFERENCE SCHEMES FOR THE POISSON-NERNST-PLANCK EQUATIONS
Creator: Flavell, Allen
Date: 2014, 2014-07
Description: The Poisson-Nernst-Planck equations are a system of nonlinear di erential equations that describe ow of charged particles in solution. This...
Show moreThe Poisson-Nernst-Planck equations are a system of nonlinear di erential equations that describe ow of charged particles in solution. This dissertation is about the design of numerical schemes to solve this system which preserves global properties exhibited by the system. There are two major advances presented. The rst is the design of schemes that conserve mass globally when the system is coupled with no- ux boundary conditions. Most notably, a scheme using central di erencing and TR-BDF2 achieves second order accuracy in both space and time, while also conserving global mass is presented. The second is the design of a more general scheme that preserves the time-varying properties of the free energy of the system. One such a scheme uses central di erencing in space and trapezoidal integration in time to achieve second order accuracy in both space and time, while also preserving the energy dynamics, but at the cost of requiring positivity of the solution. There is also a discussion of solution methods: the classic Newton iteration scheme is compared with a modi ed Gummel iteration scheme for the purpose of solving the transient equations. The intended application of this work is the modeling of ion channels, and many of the simulations presented use parameters consistent with models of ion channels.
Ph.D. in Applied Mathematics, July 2014
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