Due to an increased amount of applications that can be modeled as large-scale, there has been growing interest in using simple methods for optimization that require low iteration cost as well as limited memory storage. We will be concerned with optimization problems for networked systems with high dimensions, focusing on applications in crowdsourcing and pandemic control. What makes these problems complex is that the objectives relate to aspects of the evolution of the dynamics of the system. We develop first-order optimization methods with low iteration complexity for such applications in this dissertation work. In the first part of this work, we consider the adversarial crowdsourcing problem. We reduce this problem to the robust rank-one matrix completion problem, and we propose a new first-order algorithm with theoretical guarantees. These results are then applied to the problem of classification from crowdsourced data under the assumption that while the majority of the workers are governed by the standard single-coin David-Skene model, some of the workers can deviate arbitrarily from this model. Extensive experimental results show our algorithm outperforms all other state-of-the-art methods in such an adversarial scenario. In the second part of the work, we consider the optimal lockdown problem for pandemic control. As a common strategy of contagious disease containment, lockdowns will inevitably weaken the economy. Here we propose a mathematical framework with first-order methods to achieve pandemic control through an optimal stabilizing non-uniform lockdown, where our goal is to reduce the economic activity as little as possible while decreasing the number of infected individuals at a prescribed rate. We demonstrate the power of this framework by analyzing a model of COVID-19 spread in the 62 counties of New York State. We find that an optimal stabilizing lockdown based on epidemic status in April 2020 would have reduced economic activity more stringently outside of New York City compared to within it, even though the epidemic was much more prevalent in New York City at that point. In the third part of the work, we consider the optimal vaccine allocation issue for pandemic control, where our goal is to send the infections to zero as soon as possible with a fixed number of vaccines. To achieve this, we propose a mathematical framework for classical epidemic models as well as a COVID-19 model. Moreover, we also analyzed the epidemic model used in [Bubar et al., 2021], and compared our method with the strategies in [Bubar et al., 2021]. We found that it is better to offer vaccines to younger people when the basic reproduction number R0 is moderately above one.

Cheyne-Stokes respiration is a distinct breathing pattern consisting of periods of hyperpnea followed by apneas, with unknown etiology. One in two patients with congestive heart failure suffer from this condition. Researchers hypothesize that key factors in CSR are the fluid shift from the standing to supine position and the differences between genders. A mathematical model of the cardio-respiratory system was constructed using parameter values from real data. Hopf bifurcation analysis was used to determine regions of stable versus oscillatory breathing patterns. In the model, Cheyne-Stokes respiration is more likely to occur while in the supine position and males are more likely to develop Cheyne-Stokes than females. These findings, which are in agreement with clinical experience, suggest that both gender and fluid shift contribute to the pathogenesis of Cheyne-Stokes respiration, and that physical quantities such as blood volumes and neural feedback may be sufficient to explain the observations of CSR. / Department of Mathematics and Statistics

The abuse of and dependence on opioids are major public health problems, and have been the focus of intense media coverage and scholarly inquiry. This research explores the problem in Iowa through the lens of infectious disease modeling. We wanted to identify the current state of the crisis, factors affecting the progression of the addiction process, and evaluate interventions as data becomes available. We introduced a novel sequential Approximate Bayesian Computation technique to address shortcomings of existing methods in this complex problem space, after surveying the literature for available Bayesian computation techniques. A spatial compartmental model was used which allowed forward and backward progression through susceptible, exposed, addicted, and removed disease states. Data for this model were compiled over the years 2006-2016 for Iowa counties, from a variety of sources. Prescription overdose deaths and treatment data were obtained from the Iowa Department of Public Health, possession and distribution arrest data were acquired from the Iowa Department of Public Safety, a measure of total available pain reliever prescriptions was derived from private health insurance claims data, and population totals were obtained from the US Census Bureau. Inference was conducted in a Bayesian framework. A measure called the empirically adjusted reproductive number which estimates the expected number of new users generated from a single user was used to examine the growth of the crisis. Results expose the trend in recruitment of new users, and peak recruitment times. While we identify an overall decrease in the rate of spread during the study period, the scope of the problem remains severe, and interesting outlying trends require further investigation. In addition, an examination of the reproductive numbers estimated for contact within and between counties indicates that medical exposure, rather than spread through social networks, may be the key driver of this crisis.

京都大学 / 新制・課程博士 / 博士(農学) / 甲第23950号 / 農博第2499号 / 新制||農||1091(附属図書館) / 学位論文||R4||N5385(農学部図書室) / 京都大学大学院農学研究科森林科学専攻 / (主査)准教授 岡田 直紀, 教授 井鷺 裕司, 教授 柴田 昌三 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

La tomographie par émission de positons (TEP) est une méthode d’imagerie fonctionnelle, utilisée en particulier lors du développement de nouveaux médicaments et pour imager les tumeurs. En TEP, l’estimation de la concentration plasmatique artérielle d’activité du traceur non métabolisé (nommée « fonction d’entrée ») est nécessaire pour l’extraction des paramètres pharmacocinétiques. Ceux-ci permettent de quantifier le comportement du traceur dans les tissus, ou plus précisément le traitement du traceur par les tissus. Cette thèse constitue une contribution à l’étude de la fonction d’entrée, par l’élaboration d’une méthode d’estimation de la fonction d’entrée peu invasive à partir des images TEP et de prélèvements veineux. L’exemple du traceur FDG (analogue du glucose) dans le cerveau humain a été choisi. La méthode proposée repose sur la modélisation compartimentale de l’organisme : elle déconvolue le modèle à trois compartiments utilisé pour le FDG. L’originalité de la méthode repose sur trois points : l’utilisation d’un grand nombre de régions d’intérêt ; l’utilisation d’un grand nombre de jeux de trois régions d’intérêt différentes; une estimation itérative. Pour la validation de la méthode, un soin particulier a été porté à la simulation d’images TEP (simulation d’acquisition, reconstruction, corrections) de plus en plus réalistes, depuis une image simple simulée avec un simulateur analytique jusqu’à une image la plus proche possible de la réalité, simulée avec simulateur Monte-Carlo. Une chaîne de pré-traitement (segmentation des IRM associés, recalage entre images TEP et IRM et correction de l’effet de volume partiel par une variante de la méthode de Rousset) a ensuite été appliquée à ces images afin d’extraire les cinétiques des régions d’intérêt, données d’entrée de la méthode d’estimation de la fonction d’entrée. L’évaluation de la méthode sur différentes données, simulées et réelles, est présentée, ainsi que l’étude de la sensibilité de la méthode à différents facteurs tels que les erreurs de segmentation, de recalage, de mesure de l’activité des prélèvements sanguins. / Positron Emission Tomography (PET) is a method of functional imaging, used in particular for drug development and tumor imaging. In PET, the estimation of the arterial plasmatic activity concentration of the non-metabolized compound (the "input function") is necessary for the extraction of the pharmacokinetic parameters. These parameters enable the quantification of the compound dynamics in the tissues. This PhD thesis contributes to the study of the input function by the development of a minimally invasive method to estimate the input function. This method uses the PET image and a few blood samples. In this work, the example of the FDG tracer is chosen. The proposed method relies on compartmental modeling: it deconvoluates the three-compartment-model. The originality of the method consists in using a large number of regions of interest (ROIs), a large number of sets of three ROIs, and an iterative process. To validate the method, simulations of PET images of increasing complexity have been performed, from a simple image simulated with an analytic simulator to a complex image simulated with a Monte-Carlo simulator. After simulation of the acquisition, reconstruction and corrections, the images were segmented (through segmentation of an IRM image and registration between PET and IRM images) and corrected for partial volume effect by a variant of Rousset’s method, to obtain the kinetics in the ROIs, which are the input data of the estimation method. The evaluation of the method on simulated and real data is presented, as well as a study of the method robustness to different error sources, for example in the segmentation, in the registration or in the activity of the used blood samples.

>Magister Scientiae - MSc / Herbal medicines have been an important part of health and wellness for hundreds of years. Recently the World Health Organization estimated that 80% of people worldwide rely on herbal medicines. Herbs contain many substances that are good for protecting the body and are therefore used in the treatment of various illnesses. Along with traditional medicines, herbs are often used in the treatment of chronic diseases such as rheumatism, migraine, chronic fatigue, asthma, eczema, and irritable bowel syndrome, among others. Herbal medicines are also applied in certain traditional communities as treatment against infectious diseases such as flu, malaria, measles, and even human immunodeficiency virus HIV-infection. Approximately 34 million people are currently infected with the human immunodeficiency virus (HIV) and 2.5 million newly infected. Therefore, HIV has become one of the major public health problems worldwide. It is important to understand the impact of herbal medicines used on HIV/AIDS. Mathematical models enable us to make predictions about the qualitative behaviour of disease outbreaks and evaluation of the impact of prevention or intervention strategies. In this dissertation we explore mathematical models for studying the effect of usage of herbal medicines on HIV. In particular we analyze a mathematical model for population dynamics of HIV/AIDS. The latter will include the impact of herbal medicines and traditional healing methods. The HIV model exhibits two steady states; a trivial steady state (HIV-infection free population) and a non-trivial steady state (persistence of HIV infection). We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. Furthermore, we investigate for optimal control strategies. We study a stochastic version of the deterministic model by introducing white noise and show that this model has a unique global positive solution. We also study computationally the stochastic stability of the white noise perturbation model. Finally, qualitative results are illustrated by means of numerical simulations. Some articles from the literature that feature prominently in this dissertation are [14] of Cai et al, [10] of Bhunu et al., [86] of Van den Driessche and Watmough, [64] of Naresh et al., Through the study in this dissertation, we have prepared a research paper [1], jointly with the supervisors to be submitted for publication in an accredited journal. The author of this dissertation also contributed to the research paper [2], which close to completion. 1. Abdulaziz Y.A. Mukhtar, Peter J. Witbooi and Gail D. Hughes. A mathematical model for population dynamics of HIV with ARV and herbal medicine. 2. P.J. Witbooi, T. Seatlhodi, A.Y.A. Mukhtar, E. Mwambene. Mathematical modeling of HIV/AIDS with recruitment of infecteds.

>Magister Scientiae - MSc / In this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math- ematical model that describes the dynamics of HIV infection among the im- migrant youths and intervention that can minimize or prevent the spread of the disease in the population. In particular, we are interested in the effects of public-health education and of parental care.We consider existing models of public-health education in HIV/AIDS epidemi-ology, and provide some new insights on these. In this regard we focus atten-tion on the papers [b] and [c], expanding those researches by adding sensitivity analysis and optimal control problems with their solutions.Our main emphasis will be on the effect of parental care on HIV/AIDS epidemi-ology. In this regard we introduce a new model. Firstly, we analyse the model without parental care and investigate its stability and sensitivity behaviour.We conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is asymptotically stable. Further, we use optimal control methods to determine the necessary conditions for the optimality of intervention, and for disease eradication or control. Using Pontryagin’s Maximum Principle to check the effects of screening control and parental care on the spread of HIV/AIDS, we observe that parental care is more effective than screening control. However, the most efficient control strategy is in fact a combination of parental care and screening control. The results form the central theme of this thesis, and are included in the manuscript [a] which is now being reviewed for publication. Finally, numerical simulations are performed to illustrate the analytical results.

Cerebral blood flow quantification is a vital diagnostic tool for disease monitoring and used for diagnosing a variation of pathological conditions. The human brain requires roughly about 20 % of the total cardiac output to sustain normal functioning, hence the perfusion of blood is an important factor to deliver oxygenated blood. The golden standard for quantifying the cerebral blood flow follows by measurement with dynamic positron emission tomography of 15O-labelled water modelled by tracer kinetic compartments. For implementation, knowledge of an input function must exist which is in general being sampled through arterial cannulation of the radial artery with a continuous sampling instrument. The core of this thesis is to establish if two sampling instruments contradicts in comparison to each other when sampling the data to the input function.  In total 22 subjects underwent a 10-minute dynamic  15O-labeled water brain PET scan on two imaging modalities PET/CT and PET/MR. Continuous arterial sampling was performed either by a Veenstra on PET/CT or a Swisstrace on PET/MR during a baseline scan. In two subjects the two sampling instruments were coupled in series and imaged solely on the PET/CT.  Cerebral blood flow analysis was done comparing varying dispersion times, the two imaging modalities compared each other and comparing the calculated and measured blood flows obtained through this study with the values obtained prior. To be able to compare the values showing inconsistency to the values obtained through this thesis, a comparison between two different iterative reconstruction methods was done. Here the method of ordered subsets expectation maximum was compared to a Bayesian penalized-likelihood method. To further compare the two sampling instruments an image derived input function was constructed and compared with the blood sampled input function. The results showed that there was no significant difference between measured cerebral blood flow between the two imaging modalities with the currently used reconstruction method based on Bayesian penalized likelihood but presented in the earlier data there was an inconsistency. A dispersion analysis with variation on the external dispersion time shows that if the time was chosen to low or to high compared to the standard time used it introduced distorted fitted models of the activity curves. This distortion creates further errors in the calculation of the cerebral blood flow, however with the analysis the standard dispersion time could be confirmed as an accurate fit. Subjects imaged with the two sampling instruments in series showed no significant difference except for the measured values on Veenstra to be slightly higher. Lastly the correlation between the image derived input function and the blood sampled input function showed poorly performance. Only a R2 value of 0.42 was achieved on the PET/CT while a meagre R2 value of 0.18 was achieved on the PET/MR. Although the correlation was poorly, the plotted activity curves from the two functions showed a representable appearance between each other. / Kvantifiering av det cerebrala blodflödet är ett nödvändigt diagnostiskt verktyg som används för att kontrollera och diagnostisera en variation av patologiska sjukdomstillstånd. Den mänskliga hjärnan kräver kring 20 %av den totala produktionen från hjärtat för att upprätthålla normal funktion, följaktligen är perfusion av blod en viktig faktor för att distribuera syrerikt blod runt om i kroppen. Den gyllene standarden för kvantifiering av det cerebrala blodflödet följer som undersökning med dynamisk positron emission tomografi av 15O-märkt vatten, modellerat  med kinetisk kompartment teori. För att kunna implementera detta måste information om en input-funktion erhållas, generellt erhålls detta genom att blod tags genom arteriell kanylering av antingen den radiella artären med ett kontinuerligt samplings instrument. Målet med detta arbete är att fastställa om två samplings instrument motsäger varandra vid mätning av data till input-funktionen. Totalt deltagande är 22 patienter som genomgick en 10-minuters dynamisk 15O-märkt vatten PET undersökning av hjärnan på två bildtagningsmodaliteter PET/CT och PET/MR. Kontinuerlig blodtagning genomfördes antingen med en Veenstra sampler instrument på PET/CT eller en Swisstrace sampler instrument på PET/MR tillsammans med en baseline undersökning. Vid två undersökningar seriekopplades de två instrumenten och patienterna blev endast undersökta vid PET/CT. För ytterligare kunna utvärdera de två instrumenten, konstruerades en bild framtagen input-funktion som sedan kunde jämföras med den blod samplade input-funktionen. Cerebrala blodflödes analyser gjordes med olika dispersions tider, även för att kunna jämföra de två bildtagningsmodaliteterna mot varandra och jämföra erhållna värden framtagna under denna studie med en tidigare studie. För att kunna jämföra avvikelserna i de uppmätta värdena har även två olika rekonstruerings metoder studerats. Resultaten visar ingen signifikant skillnad mellan de uppmätta cerebrala blodflödena mellan de två bildtagningsmodaliteterna rekonstruerade med den nuvarande standarden. Dispersions analysen med varierande extern dispersions tid visar att om tiden är för kort eller för lång jämfört med standardtiden, introduceras en osann anpassning av aktivitets kurvorna. Denna förvrängning av datat resulterar till fler avvikelser i beräkningarna av blodflödet, likväl var det möjligt att bekräfta standardtiderna som används. Patienter som undersöktes med instrumenten i seriekoppling visade ingen signifikant skillnad förutom att det uppmättes en aningens högre värden hos patienter med Veenstra som blod sampler. Slutligen, korrelationen mellan den bild framtagna input-funktionen och den blod samplade input-funktionen visade ett dåligt resultat. Endast ett R2 värde på 0.42 erhölls för PET/CT medan endast ett R2 värde på 0.18 på PET/MR erhölls. Trotts att korrelationen var dålig, visade de plottade aktivitets kurvorna ett representativt utseende mellan de två typerna av input funktion.