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Yes / The FCC riser cracks gas oil into useful fuels such as gasoline, diesel and some lighter products such as ethylene and propylene, which are major building blocks for the polyethylene and polypropylene production. The production objective of the riser is usually the maximization of gasoline and diesel, but it can also be to maximize propylene. The optimization and parameter estimation of a six-lumped catalytic cracking reaction of gas oil in FCC is carried out to maximize the yield of propylene using an optimisation framework developed in gPROMS software 5.0 by optimizing mass flow rates and temperatures of catalyst and gas oil. The optimal values of 290.8 kg/s mass flow rate of catalyst and 53.4 kg/s mass flow rate of gas oil were obtained as propylene yield is maximized to give 8.95 wt%. When compared with the base case simulation value of 4.59 wt% propylene yield, the maximized propylene yield is increased by 95%.

Parameter estimation is a pivotal task across various domains such as system identification, statistics, and machine learning. The literature presents numerous estimation procedures, many of which are backed by well-studied asymptotic properties. In the contemporary landscape, highly advanced digital twins (DTs) offer the capability to faithfully replicate real systems through proper tuning. Leveraging these DTs, data-driven estimators can alleviate challenges inherent in traditional methods, notably their computational cost and sensitivity to initializations. Furthermore, traditional estimators often rely on sensitive data, necessitating protective measures. In this thesis, we consider data-driven and privacy-preserving approaches to parameter estimation that overcome many of these challenges. The first part of the thesis delves into an exploration of modern data-driven estimation techniques, focusing on the two-stage (TS) approach. Operating under the paradigm of inverse supervised learning, the TS approach simulates numerous samples across parameter variations and employs supervised learning methods to predict parameter values. Divided into two stages, the approach involves compressing data into a smaller set of samples and the second stage utilizes these samples to predict parameter values. The simplicity of the TS estimator underscores its interpretability, necessitating theoretical justification, which forms the core motivation for this thesis. We establish statistical frameworks for the TS estimator, yielding its Bayes and minimax versions, alongside developing an improved minimax TS variant that excels in computational efficiency and robustness to distributional shifts. Finally, we conduct an asymptotic analysis of the TS estimator. The second part of the thesis introduces an application of data-driven estimation methods, that includes the TS and neural network based approaches, in the design of tuning rules for PI controllers. Leveraging synthetic datasets generated from DTs, we train machine learning algorithms to meta-learn tuning rules, streamlining the calibration process without manual intervention. In the final part of the thesis, we tackle scenarios where estimation procedures must handle sensitive data. Here, we introduce differential privacy constraints into the Bayes point estimation problem to protect sensitive information. Proposing a unified approach, we integrate the estimation problem and differential privacy constraints into a single convex optimization objective, thereby optimizing the accuracy-privacy trade-off. In cases where both observations and parameter spaces are finite, this approach reduces to a tractable linear program which is solvable using off-the-shelf solvers. In essence, this thesis endeavors to address computational and privacy concerns within the realm of parameter estimation. / Skattning av parametrar utgör en fundamental uppgift inom en mängd fält, såsom systemidentifiering, statistik och maskininlärning. I litteraturen finns otaliga skattningsmetoder, utav vilka många understödjs av välstuderade asymptotiska egenskaper. Inom dagens forskning erbjuder noggrant kalibrerade digital twins (DTs) möjligheten att naturtroget återskapa verkliga system. Genom att utnyttja dessa DTs kan data-drivna skattningsmetoder minska problem som vanligtvis drabbar traditionella skattningsmetoder, i synnerhet problem med beräkningsbörda och känslighet för initialiseringvillkor. Traditionella skattningsmetoder kräver dessutom ofta känslig data, vilket leder till ett behov av skyddsåtgärder. I den här uppsatsen, undersöker vi data-drivna och integritetsbevarande parameterskattningmetoder som övervinner många av de nämnda problemen.  Första delen av uppsatsen är en undersökning av moderna data-drivna skattningtekniker, med fokus på två-stegs-metoden (TS). Som metod inom omvänd övervakad maskininlärning, simulerar TS en stor mängd data med ett stort urval av parametrar och tillämpar sedan metoder från övervakad inlärning för att förutsäga parametervärden. De två stegen innefattar datakomprimering till en mindre mängd, varefter den mindre mängden data används för parameterskattning. Tack vare sin enkelhet och tydbarhet lämpar sig två-stegs-metoden väl för teoretisk analys, vilket är uppsatsens motivering. Vi utvecklar ett statistiskt ramverk för två-stegsmetoden, vilket ger Bayes och minimax-varianterna, samtidigt som vi vidareutvecklar minimax-TS genom en variant med hög beräkningseffektivitet och robusthet gentemot skiftade fördelningar. Slutligen analyserar vi två-stegs-metodens asymptotiska egenskaper.  Andra delen av uppsatsen introducerar en tillämpning av data-drivna skattningsmetoder, vilket innefattar TS och neurala nätverk, i designen och kalibreringen av PI-regulatorer. Med hjälp av syntetisk data från DTs tränar vi maskininlärningsalgoritmer att meta-lära sig regler för kalibrering, vilket effektiverar kalibreringsprocessen utan manuellt ingripande.  I sista delen av uppsatsen behandlar vi scenarion då skattningsprocessen innefattar känslig data. Vi introducerar differential-privacy-begränsningar i Bayes-punktskattningsproblemet för att skydda känslig information. Vi kombinerar skattningsproblemet och differential-privacy-begränsningarna i en gemensam konvex målfunktion, och optimerar således avvägningen mellan noggrannhet och integritet. Ifall både observations- och parameterrummen är ändliga, så reduceras problemet till ett lätthanterligt linjärt optimeringsproblem, vilket löses utan vidare med välkända metoder.  Sammanfattningsvis behandlar uppsatsen beräkningsmässiga och integritets-angelägenheter inom ramen för parameterskattning. / <p>QC 20240306</p>

This thesis provides insight into methods for estimating blood perfusion, emphasizing the need for accurate modeling in dynamic physiological environments. The thesis critically examines conventional error function solutions used in steady state or gradually changing blood flow scenarios, revealing their shortcomings in accurately reflecting more rapid changes in blood perfusion. To address this limitation, this study introduces a novel prediction model based on the finite-difference method (FDM) specifically designed to produce accurate results under different blood flow perfusion conditions. A comparative analysis concludes that the FDM-based model is consistent with traditional error function methods under constant blood perfusion conditions, thus establishing its validity under dynamic and steady blood flow conditions. In addition, the study attempts to determine whether analytical solutions exist that are suitable for changing perfusion conditions. Three alternative analytical estimation methods were explored, each exposing the common thread of inadequate responsiveness to sudden changes in blood perfusion. Based on the advantages and disadvantages of the error function and FDM estimation, a combination of these two methods was developed. Utilizing the simplicity and efficiency of the error function, the prediction of contact resistance and core temperature along with the initial blood perfusion was first made at the beginning of the data. Then the subsequent blood perfusion values were predicted using the FDM, as the FDM can effectively respond to changing blood perfusion values. / Master of Science / Blood perfusion, the process of blood flowing through our body's tissues, is crucial for our health. It's like monitoring traffic flow on roads, which is especially important during rapid changes, such as during exercise or medical treatments. Traditional methods for estimating blood perfusion, akin to older traffic monitoring techniques, struggle to keep up with these rapid changes. This research introduces a new approach, using a method often found in engineering and physics, called the finite-difference method (FDM), to create more accurate models of blood flow in various conditions. This study puts this new method to the test against the old standards. We discover that while both are effective under steady conditions, the FDM shines when blood flow changes quickly. We also examined three other methods, but they, too, fell short in these fast-changing scenarios. This work is more than just numbers and models; it's about potentially transforming how we understand and manage health. By combining the simplicity of traditional methods for initial blood flow estimates with the dynamic capabilities of the FDM, we're paving the way for more precise medical diagnostics and treatments.

The STREAMC model is based on the same algorithm as implemented by the Steady Riverine Environmental Assessment Model (STREAM), a mathematical model for the dissolved oxygen (DO) distribution in freshwater streams used by Mississippi Department of Environmental Quality (MDEQ). Typically the water quality models are calibrated manually. In some cases where some objective criterion can be identified to quantify a successful calibration, an auto calibration may be preferable to the manual calibration approach. The auto calibration may be particularly applicable to relatively simple analytical models such as the steady-state STREAMC model. Various techniques of parameter estimation were identified for the model. The model was then subjected to various techniques of parameter estimation identified and/or developed. The parameter estimates obtained by different techniques were tabulated and compared. A final recommendation regarding a preferable parameter estimation technique leading to the auto calibration of the STREAMC model was made.

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Yes / Polypropylene is one type of plastic that is widely used in our everyday life. This study focuses on the identification and justification of the optimum process parameters for polypropylene production in a novel pilot plant based fluidized bed reactor. This first-of-its-kind statistical modeling with experimental validation for the process parameters of polypropylene production was conducted by applying ANNOVA (Analysis of variance) method to Response Surface Methodology (RSM). Three important process variables i.e., reaction temperature, system pressure and hydrogen percentage were considered as the important input factors for the polypropylene production in the analysis performed. In order to examine the effect of process parameters and their interactions, the ANOVA method was utilized among a range of other statistical diagnostic tools such as the correlation between actual and predicted values, the residuals and predicted response, outlier t plot, 3D response surface and contour analysis plots. The statistical analysis showed that the proposed quadratic model had a good fit with the experimental results. At optimum conditions with temperature of 75 °C, system pressure of 25 bar and hydrogen percentage of 2%, the highest polypropylene production obtained is 5.82% per pass. Hence it is concluded that the developed experimental design and proposed model can be successfully employed with over a 95% confidence level for optimum polypropylene production in a fluidized bed catalytic reactor (FBCR).

Circadian rhythms are the endogenous, roughly 24-hour rhythms that coordinate an organism's interaction with its cycling environment. The molecular mechanism underlying this physiological process is a cell-autonomous oscillator comprised of a complex regulatory network of interacting DNA, RNA and proteins that is surprisingly conserved across many different species. It is not a trivial task to understand how the positive and negative feedback loops interact to generate an oscillator capable of a) maintaining a 24-hour rhythm in constant conditions; b) entraining to external light and temperature signals; c) responding to pulses of light in a rather particular, predictable manner; and d) compensating itself so that the period is relatively constant over a large range of temperatures, even for mutations that affect the basal period of oscillation. Mathematical modeling is a useful tool for dealing with such complexity, because it gives us an object that can be quickly probed and tested in lieu of the experiment or actual biological system. If we do a good job designing the model, it will help us to understand the biology better by predicting the outcome of future experiments. The difficulty lies in properly designing a model, a task that is made even more difficult by an acute lack of quantitative data. Thankfully, our qualitative understanding of a particular phenomenon, i.e. the observed physiology of the cell, can often be directly related to certain mathematical structures. Bifurcation analysis gives us a glimpse of these structures, and we can use these glimpses to build our models with greater confidence. In this dissertation, I will discuss the particular problem of the circadian clock and describe a number of new methods and tools related to bifurcation analysis. These tools can effectively be applied during the modeling process to build detailed models of biological regulatory with greater ease. / Ph. D.

Fertilized frog eggs (and cell-free extracts) undergo periodic oscillations in the activity of "M-phase promoting factor" (MPF), the crucial triggering enzyme for mitosis (nuclear division) and cell division. MPF activity is regulated by a complex network of biochemical reactions. Novak and Tyson, and their collaborators, have been studying the qualitative and quantitative properties of a large system of nonlinear ordinary differential equations that describe the molecular details of this system as currently known. Important clues to the behavior of the model are provided by bifurcation theory, especially characterization of the codimension-1 and -2 bifurcation sets of the differential equations. To illustrate this method, I have been studying a system of 9 ordinary differential equations that describe the frog egg cell cycle with some fidelity. I will describe the bifurcation diagram of this system in a parameter space spanned by the rate constants for cyclin synthesis and cycling degradation. My results suggest either that the cell cycle control system should show dynamical behavior considerably more complex than the limit cycles and steady states reported so far, or that the biochemical rate constants of the system are constrained to avoid regions of parameter space where complex bifurcation points unfold. / Ph. D.