Polymeric microchips have received increasing attention in chemical analysis because polymers have attractive properties, such as low cost, ease of fabrication, biocompatibility and high flexibility. However, commercial polymers usually exhibit analyte adsorption on their surfaces, which can interfere with microfluidic transport in, for example, chemical separations such as chromatography or electrophoresis. Usually, surface modification is required to eliminate this problem. To perform stable and durable surface modification, a new polymer, poly(methyl methacrylate-co-glycidyl methacrylate) (PGMAMMA) was prepared for microchip fabrication, which provides epoxy groups on the surface. Whole surface atom transfer radical polymerization (ATRP) and in-channel ATRP approaches were employed to create uniform and dense poly(ethylene glycol) (PEG)-functionalized polymer brush channel surfaces for capillary electrophoresis (CE) separation of biomolecules, such as peptides and proteins. In addition, a novel microchip material was developed for bioanalysis, which does not require surface modification, made from a PEG-functionalized copolymer. The fabrication is easy and fast, and the bonding is strong. Microchips fabricated from this material have been applied for CE separation of small molecules, peptides, proteins and enantiomers. Electric field gradient focusing (EFGF) is an attractive technique, which depends on an electric field gradient and a counter-flow to focus, concentrate and separate charged analytes, such as peptides and proteins. I used the PEG-functionalized copolymer to fabricate EFGF substrates. The separation channel was formed in an ionically conductive and protein resistant PEG-functionalized hydrogel, which was cast in a changing cross-sectional cavity in the plastic substrate. The hydrogel shape was designed to create linear or non-linear gradients. These EFGF devices were successfully used for protein focusing, and their performance was optimized. Use of buffers containing small electrolyte ions promoted rapid ion transport in the hydrogel for achieving the designed gradients. A PEG-functionalized monolith was incorporated in the EFGF separation channel to reduce dispersion and improve focusing performance. Improvement in peak capacity was proposed using a bilinear EFGF device. Protein concentration exceeding 10,000-fold was demonstrated using such devices.

<p>Stochastic Gradient Descent (SGD) is a widely-used iterative algorithm for solving stochastic optimization problems for a smooth (and possibly non-convex) objective function via queries from a first-order stochastic oracle.</p> <p>In this dissertation, we critically examine SGD's choice of executing a single step as opposed to multiple steps between subsample updates. Our investigation leads naturally to generalizing SG into Retrospective Approximation (RA) where, during each iteration, a deterministic solver executes possibly multiple steps on a subsampled deterministic problem and stops when further solving is deemed unnecessary from the standpoint of statistical efficiency. RA thus leverages what is appealing for implementation -- during each iteration, a solver, e.g., L-BFGS with backtracking line search is used, as is, and the subsampled objected function is solved only to the extent necessary. We develop a complete theory using relative error of the observed gradients as the principal object, demonstrating that almost sure and L1 consistency of RA are preserved under especially weak conditions when sample sizes are increased at appropriate rates. We also characterize the iteration and oracle complexity (for linear and sub-linear solvers) of RA, and identify two practical termination criteria, one of which we show leads to optimal complexity rates. The message from extensive numerical experiments is that the ability of RA to incorporate existing second-order deterministic solvers in a strategic manner is useful both in terms of algorithmic trajectory as well as from the standpoint of  dispensing with hyper-parameter tuning.</p>

Resource management is an important component in many distributed clusters. A resource manager handles which server a task should run on and which user’s task that should be allocated. If a system has multiple users with similar demands, all users should have an equal share of the cluster, making the system fair. This is typically done today using a centralized server which has full knowledge of all servers in the cluster and the different users. Having a centralized server brings problems such as single point of failure, and vertical scaling on the resource manager. This thesis focuses on fairness for users during task allocation with a decentralized resource manager. A solution called, Parallel Distributed Gradient-based Dominant Resource Fairness, is proposed. It allows servers to handle a subset of users and to allocate tasks in parallel, while maintaining fairness results close to a centralized server. The solution utilizes a gradient network topology overlay to sort the servers based on their users’ current usage and allows a server to know if it has the user with the currently lowest resource usage. The solution is compared to pre-existing solutions, based on fairness and allocation time. The results show that the solution is more fair than the pre-existing solutions based on the gini-coefficient. The results also show that the allocation time scales based on the number of users in the cluster because it allows more parallel allocations by the servers. It does not scale as well though as existing distributed solutions. With 40 users and over 100 servers the solution has an equal time to a centralized solution and outperforms a centralized solution with more users. / Resurshantering är en viktig komponent i många distribuerade kluster. En resurshanterare bestämmer vilken server som skall exekvera en uppgift, och vilken användares uppgift som skall allokeras. Om ett system har flera användare med liknande krav, bör resurserna tilldelas jämnlikt mellan användarna. Idag implementeras resurshanterare oftast som en centraliserad server som har information om alla servrar i klustret och de olika användarna. En centraliserad server skapar dock problem som driftstopp vid avbrott på ett enda ställe, även enbart vertikal skalning för resurshanteraren. Denna uppsats fokuserar på jämnlikhet för användare med en decentraliserad resurshanterare. En lösning föreslås, Parallel Distributed Gradient-based Dominant Resource Fairness, som tillåter servrar att hantera en delmängd av användare i systemet, detta med en liknande jämnlikhet jämförande med en centraliserad server. Lösningen använder en så kallad gradient network topology overlay för att sortera servrarna baserat på deras användares resursanvändning och tillåter en server att veta om den har användaren med lägst resursanvändning i klustret. Lösningen jämförs med existerande lösningar baserat på jämnlikhet och allokeringstid. Resultaten visar att lösningen ger en mer jämnlik allokering än existerande lösningar utifrån gini-koefficienten. Resultaten visar även att systemets skallbarhet angående allokeringstid är beroende på antalet användare i klustret eftersom det tillåter fler parallella allokeringar. Lösningen skalar inte lika bra dock som existerande distribuerade lösningar. Med 40 användare och över 100 servrar har lösningen liknande tid som en centraliserad server, och är snabbare med fler användare.

Time-of-Flight (ToF) cameras are becoming an increasingly common sensor in smartphones. These sensors are able to produce depth measurements in a grid at a relatively high rate. Using these depth measurements, point-clouds representing the captured scene can be produced. Previous research has been conducted in using ToF or LIDAR images to localize the camera. In this paper, we investigate several methods to localize the camera using point-clouds and surface meshes. Small alterations were made to some of the algorithms but the concepts remain the same. The main algorithms consisted of ICP variants as well as a relatively recent method called Corrective Gradient Refinement (CGR). The results obtained from generated data indicate that some of the methods are applicable for real-time applications, and the position estimates are comparable to those found in previous results. / Time-of-flight (ToF)-kameror blir en allt vanligare sensor i mobiltelefoner. Dessa sensorer kan producera djupmätningar i ett rutnät med relativt hög frekvens. Med hjälp av dessa djupmätningar kan ett punktmoln som representerar den fångade scenen produceras. Tidigare forskning har gjorts med hjälp av ToF- eller LIDAR-bilder för att lokalisera kameran. Här undersöks flera metoder för att lokalisera kameran med hjälp av ett punktmoln och en triangulering av en modell. Algoritmerna bestod till största delen av ICP-varianter samt en relativt ny metod som heter Corrective Gradient Refinement (CGR). Resultaten som erhållits från genererade data indikerar att vissa av metoderna är lämplig för realtidsapplikationer och felet på positioneringen är jämförbart med dem som hittades i tidigare resultat.

Many novel graph neural network models have reported an impressive performance on benchmark dataset, but the theory behind these networks is still being developed. In this thesis, we study the trajectory of Gradient descent (GD) and Stochastic gradient descent (SGD) in the loss landscape of Graph neural networks by replicating Xing et al. [1] study for feed-forward networks. Furthermore, we empirically examine if the training process could be accelerated by an optimization algorithm inspired from Stochastic gradient Langevin dynamics and what effect the topology of the graph has on the convergence of GD by perturbing its structure. We find that the loss landscape is relatively flat and that SGD does not encounter any significant obstacles during its propagation. The noise-induced gradient appears to aid SGD in finding a stationary point with desirable generalisation capabilities when the learning rate is poorly optimized. Additionally, we observe that the topological structure of the graph plays a part in the convergence of GD but further research is required to understand how. / Många nya grafneurala nätverk har visat imponerande resultat på existerande dataset, dock är teorin bakom dessa nätverk fortfarande under utveckling. I denna uppsats studerar vi banor av gradientmetoden (GD) och den stokastiska gradientmetoden (SGD) i lösningslandskapet till grafiska faltningsnätverk genom att replikera studien av feed-forward nätverk av Xing et al. [1]. Dessutom undersöker vi empiriskt om träningsprocessen kan accelereras genom en optimeringsalgoritm inspirerad av Stokastisk gradient Langevin dynamik, samt om grafens topologi har en inverkan på konvergensen av GD genom att ändra strukturen. Vi ser att lösningslandskapet är relativt plant och att bruset inducerat i gradienten verkar hjälpa SGD att finna stabila stationära punkter med önskvärda generaliseringsegenskaper när inlärningsparametern har blivit olämpligt optimerad. Dessutom observerar vi att den topologiska grafstrukturen påverkar konvergensen av GD, men det behövs mer forskning för att förstå hur.

Syftet med projektet har varit att utforma skolbyggnaderna med den tillhörande gården så att förutsättningarna för ett framgångsrikt lärande maximeras. Detta tar sig bl.a. uttryck i sambandet mellan rummen. Rummen närmast gatan är slutna och lugna för aktiviteter som kräver koncentration för att sedan gradvis bli mer öppna och ”vilda” mot gården. Alltså gradient mellan koncentration och lek. Planlösningen och rumssambanden är också uppbyggda på samma sätt, repetativt på de olika avdelningarna i syfte att skapa trygghet i igenkänningen och för att det blir lätt att orientera sig. Byggnationen/Projektet består av en lågstadiedel, en förskoledel och en publik del med matsal och sporthall. Allt präglas av småskalighet. Jag har velat skapa en intim skola, av det skälet har jag valt att bygnaderna ska var relativt låga. Jag har också valt att utnyttja tomtens närhet till naturen både rumsligt - genom att lägga gården i direkt anslutning till skogen – och genom val av material. Jag har lagt byggnaderna så nära tomtgränsen som det bara är möjligt för att kunna göra gårdsytan i mitten så stor som möjligt. Gården ytgör en gata mellan byggnaderna som innebär en naturlig möteplats för alla elever. / The purpose of the project has been to design school buildings with its courtyard so the conditions for successful learning are maximized. The relationship between the rooms are of great importance. The rooms closest to the street are closed and calm for activities that require concentration. The rooms then gradually become more open and "wild" towards the courtyard. This means it’s gradient between concentration and play. The solution for how the rooms are situated in relation to each other and the design of singles rooms are also structured in the same way, repetitively at the various departments in order to create confidence in recognition and for easy orientation.   The project consists of a low-school part, a preschool and a public part with a dining room and sports hall. Everything is characterized by small scale. I have wanted to create an intimate school and for that reason the buildings are relatively low. I have also chosen to use the proximity of the plot to nature both spatially - by laying the farm in direct connection to the forest - and by selecting materials. I have laid the buildings as close to the land boundary as it is possible to make the courtyard in the center as large as possible. The courtyard constitutes sort of a street between the buildings which provides a natural meeting place for all students.

The antibody immunoglobulin G (IgG) can be tryptically digested into smaller peptides. This study attempted to develop a separation method for those peptides using RP-HPLC with a C18 column at room temperature. Optimizing separation of trypsin cleaved cytochrome C was used as a guideline before analyzing IgG. The optimized analysis of Cytochrome C was performed at wavelength 280nm (UV) and methanol was used as an organic solvent in mobile phase (B). A fast gradient to 100% mobile phase B with low flow rate gave favorable results for cytochrome C. A slow gradient to 100% mobile phase B was suited for IgG separation. The optimized gradient elution of cytochrome C and IgG was performed at 0.3 and 0.8 ml/min, respectively. / Antikroppen Immunoglobulin G (IgG) kan klyvas till peptider med enzymet trypsin. Under denna studie ska utvecklades en separationsmetod för dessa peptider med RP-HPLC. Separationen utfördes med en C18 kolonn i rumstemperatur. Först optimerades en separation av trypsin-klyvt cytokrom C vars optimerade parametrar sedan användes som grund för IgG-separation. Optimeringen utfördes vid våglängden 280 nm(UV) och metanol användes som organiskt lösningsmedel i mobil fas (B). En snabb gradient upp till 100% B med låg flödeshastighet gav mest gynnsamt resultat för cytokrom C. Separationen av IgG gynnades av ett högt flöde och en långsam gradient till 100% B. Den optimerade gradientelueringen för cytokrom C och IgG gjordes vid flödet 0.3 respektive 0.8 ml/min.

The evaluation of prosthetic valves can provide a unique challenge, and a thoughtful approach is required. High output states like anemia should be kept in the differential when evaluating elevated gradients across prosthetic valves. We present the case of a 69-year-old man with a Starr-Edwards prosthetic aortic valve who presented with symptoms of congestive heart failure and high transvalvular pressure gradients. These symptoms indicate a potential prosthetic valve stenosis. His laboratory evaluation results were consistent with valve-related hemolysis. Resolving his anemia led to a resolution of the symptoms and lowered the pressure gradient on follow-up.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

High Reynolds number turbulent boundary layers over both smooth and rough surfaces subjected to a systematically defined family of continually varying, bi-directional pressure gradient distributions are investigated in both wind tunnel experiments and steady 2D and 3D Reynolds Averaged-Navier-Stokes (RANS) computations. The effects of pressure gradient, pressure gradient history, roughness, combined roughness and pressure gradient, and combined roughness and pressure gradient history on boundary growth and the behavior of the underlying surface pressure spectrum are examined. Special attention is paid to how said pressure spectra may be effectively modeled and predicted by assessing existing empirical and analytical modeling formulations, proposing updates to those formulations, and assessing RANS flow modeling as it pertains to successful generation of spectral model inputs. It is found that the effect of pressure gradient on smooth wall boundary layers is strongly non-local. The boundary layer velocity profile, turbulence profiles, and associated parameters and local skin friction at a point that has seen non-constant upstream pressure gradient history will be dependent both on the local Reynolds number and pressure gradient as well as the Reynolds number and pressure gradient history. This shows itself most readily in observable downstream lagging in key observed behaviors. Steady RANS solutions are capable of predicting this out-of-equilibrium behavior if the pressure gradient distribution is captured correctly, however, capturing the correct pressure gradient is not as straightforward as may have previously been thought. Wind tunnel flows are three-dimensional, internal problems dominated by blockage effects that are in a state of non-equilibrium due to the presence of corner and juncture flows. Modeling a 3D tunnel flow is difficult with the standard eddy viscosity models, and requires the Quadratic Constitutive Relation for all practical simulations. Modeling in 2D is similarly complex, for, although 3D effects can be ignored, the absence of two walls worth of boundary layer and other interaction flows causes the pressure gradient to be captured incorrectly. These effects can be accounted for through careful setup of meshed geometry. Pressure gradient and history effects on the pressure spectra beneath smooth wall boundary layers show similar non-locality, in addition to exhibiting varying effects across different spectral regions. In general, adverse pressure gradient steepens the slope of the mid-frequency region while favorable shallows it, while the high frequency region shows self-similarity under viscous normalization independent of pressure gradient. The outer region is dominated by history effects. Modeling of such spectra is not straightforward; empirical models fail to incorporate the subtle changes in spectral shape as coherent functions of flow variables without becoming overly-defined and producing non-physical spectral shapes. Adopting an analytical formulation based on the pressure Poisson equation solves this issue, but brings into play model inputs that are difficult to predict from RANS. New modeling protocols are proposed that marry the assumptions and limitations of RANS results to the analytical spectral modeling. Rough surfaces subjected to pressure gradients show simplifications over their smooth wall relatives, including the validity of Townsend's outer-layer-Reynolds-number-similarity Hypothesis and shortened history effects. The underlying pressure spectra are also significantly simplified, scaling fully on a single outer variable scaling and showing no mid-frequency slope pressure gradient dependence. This enables the development of a robust and accurate empirical model for the pressure spectra beneath rough wall flows. Despite simplifications in the flow physics, modeling rough wall flows in a steady RANS environment is a challenge, due to a lack of understanding of the relationship between the rough wall physics and the RANS model turbulence parameters; there is no true physical basis for a steady RANS roughness boundary condition. Improvements can been made, however, by tuning a shifted wall distance, which also factors heavily into the mathematical character of the pressure spectrum and enables adaptations to the analytical model formulations that accurately predict rough wall pressure spectra. This work was sponsored by the Office of Naval Research, in particular Drs. Peter Chang and Julie Young under grants N00014-18-1-2455, N00014-19-1-2109, and N00014-20-2821. This work was also sponsored by the Department of Defense Science, Mathematics, and Research for Transformation (SMART) Fellowship Program and the Naval Air Warfare Center Aircraft Division (NAWCAD), in particular Mr. Frank Taverna and Dr. Phil Knowles. / Doctor of Philosophy / Very near to a solid surface, air or water flow tends to be highly turbulent: chaotic and random in nature. This is called a boundary layer, which is present on almost every system that involves a fluid and a solid with motion between them. When the boundary layer is turbulent, the surface of the solid body experiences pressures that fluctuate very rapidly, and this can fatigue the structure and create noise that radiates both into the structure to passengers and out from the structure to observers far away. These pressure fluctuations can be described in a statistical nature, but these statistics are not well understood, particularly when the surface is rough or the average pressure on the surface is changing. Improving the ability to predict the statistics of the pressure fluctuations will aid in the design of vehicles and engineering systems where those fluctuations can be damaging to the structure or the associated noise is detrimental to the role of the system. Wind turbine farm noise, airport community noise, and air/ship-frame longevity are all issues that stand to benefit from improved modeling of surface pressure fluctuations beneath turbulent boundary layers. This study aims to improve said modeling through the study of the effects of changing average surface pressure and surface roughness on the statistics of surface pressure fluctuations. This goal is accomplished through a combination of wind tunnel testing and computer simulation. It was found that the effect of gradients in the surface pressure is not local, meaning the effects are felt by the boundary layer at a different point than where the gradient was actually applied. This disconnect between cause and effect makes understanding and modeling the flow challenging, but adjustments to established modeling ideas are proposed that prove more effective than what exists in the literature for capturing those effects. Roughness on the surface causes the flow to become even more turbulent and the surface pressure fluctuations to become louder and more damaging. Fortunately, it is found that the combination of roughness with a gradient in surface pressure is actually simpler than equivalent smooth surfaces. These simplifications offer significant insight into the underlying physics at play and enable the development of the first analytically based model for rough wall pressure fluctuations.