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Cellular decision-making help cells to infer functionally different phenotypes in response to microenvironmental cues and noise present in the system and the environment, with or without genetic change. In Cellular Biology, there exists a list of open questions such as, how individual cell decisions influence the dynamics at the population level (an organization of indistinguishable cells) and at the tissue level (a group of nearly identical cells and their corresponding extracellular matrix which simultaneously accomplish a set of biological operations)? As collective cell migration originates from local cellular orientation decisions, can one generate a mathematical model for collective cell migration phenomena without elusive undiscovered biophysical/biochemical mechanisms and further predict the pattern formations which originates inside the collective cell migration? how optimal microenvironmental sensing is related to differentiated tissue at the spatial scale ? How cell sensing radius and total entropy production (which precisely helps us to understand the operating regimes where cells can take decisions about their future fate) is correlated, and how can one understand the limits of sensing radius at robust tissue development ? To partially tackle these sets of questions, the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis has been applied to different biological scenaros. At first, the LEUP has been enforced to understand the spatio-temporal behavior of a tissue exhibiting phenotypic plasticity (it is a prototype of cell decision-making). Here, two cases have been rigorously studied i.e., migration/resting and migration/proliferation plasticity which underlie the epithelial-mesenchymal transition (EMT) and the Go-or-Grow dichotomy. On the one hand, for the Go-or-Rest plasticity, a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase has been observed from an analogous mean-field approximation which further depends on the sensitivity of the phenotypes to the microenvironment. However, on the other hand, for the Go-or-Grow plasticity, the possibility of Turing pattern formation is inspected for the “solid” tissue phase and its relation to the parameters of the LEUP-driven cell decisions. Later, LEUP hypothesis has been suggested in the area of collective cell migration such that it can provide a tool for a generative mathematical model of collective migration without precise knowledge about the mechanistic details, where the famous Vicsek model is a special case. In this generative model of collective cell migration, the origin of pattern formation inside collective cell migration has been investigated. Moreover, this hypothesis helps to construct a mathematical model for the collective behavior of spherical \textit{Serratia marcescens} bacteria, where the basic understanding of migration mechanisms remain unknown. Furthermore, LEUP has been applied to understand tissue robustness, which in turn shows the way how progenitor cell fate decisions are associated with environmental sensing. The regulation of environmental sensing drives the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue, which are verified later with the experimental data. LEUP driven stochastic thermodynamic formalism also shows that the thermodynamic robustness of differentiated tissues depends on cell metabolism, cell sensing properties and the limits of the cell sensing radius, which further ensures the robustness of differentiated tissue spatial order. Finally, all important results of the thesis have been encapsulated and the extension of the LEUP has been discussed.:Contents Statement of authorship vii Abstract ix I. Introduction to cell decision-making 1 1. What is cell decision-making ? 3 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2. Examplesofcelldecision-making. . . . . . . . . . . . . . . . . . . . . . 4 1.2.1. PhenotypicPlasticity . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2. Cellularmigration:orientationdecisions . . . . . . . . . . . . . 5 1.2.3. Celldifferentiation . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3. Challengesandopenquestions . . . . . . . . . . . . . . . . . . . . . . 7 1.4. Solutionstrategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5. Structureofthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 II. Least microEnvironmental Uncertainty Principle (LEUP) 11 2. Least microEnvironmental Uncertainty Principle (LEUP) 13 2.1. HypothesisbehindLEUP . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2. Mathematicalformulation . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1. CellasBayesiandecisionmaker . . . . . . . . . . . . . . . . . . 14 2.2.2. VariationalprincipleforLEUP . . . . . . . . . . . . . . . . . . . . 16 III. LEUP in biological problems 17 3. Phenotypic plasticity : dynamics at the level of tissue from individual cell decisions 19 3.1. Mathematicalframework . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2. Individualbasedmodel(IBM) . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3. Mean-fieldapproximation . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1. Phenotypicswitchingdynamics . . . . . . . . . . . . . . . . . . 26 3.3.2. Cellmigrationdynamics . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.3. Superpositionofphenotypicswitchingdynamicsandcellmi- gration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4. Spatio-temporaldynamicsofcellmigration/proliferationplasticity . . 28 3.4.1. CaseI:Largeinteractionradius . . . . . . . . . . . . . . . . . . 29 3.4.2. CaseII:Finiteinteractionradius . . . . . . . . . . . . . . . . . . 30 3.4.3. Phenotypicswitchingdynamicsintheabsenceofmicroenvi- ronmentalsensing . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5. Summaryandoutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4. Cellular orientation decisions: origin of pattern formations in collective cell migrations 39 4.1. Mathematicalframework . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1. Self-propelledparticlemodelwithleupbaseddecision-making 41 4.1.2. Orderparametersandobservables . . . . . . . . . . . . . . . . 42 4.1.3. Statisticaltest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2. ComparisonwithVicsekmodel . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.1. Patternsindifferentparameterregimes . . . . . . . . . . . . . 45 4.3. Application:thesphericalbacteriacase. . . . . . . . . . . . . . . . . . 47 4.4. Summaryandoutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5. Cell differentiation and sensing: tissue robustness from optimal environ- mental sensing 53 5.1. LEUPbasedmathematicalmodelforcelldifferentiation . . . . . . . . 56 5.1.1. StatisticalresultsfromLEUP . . . . . . . . . . . . . . . . . . . . 59 5.2. RelationbetweenLEUPandcellsensing . . . . . . . . . . . . . . . . . 60 5.3. LEUPdrivenfluctuationtheorem: confirmsthethermodynamicro- bustnessofdifferentiatedtissues . . . . . . . . . . . . . . . . . . . . . 61 5.3.1. Application: differentiated photoreceptor mosaics are ther- modynamicallyrobust . . . . . . . . . . . . . . . . . . . . . . . . 65 5.4. Thelimitforcellsensingradius . . . . . . . . . . . . . . . . . . . . . . . 67 5.4.1. Application:Theaveragesensingradiusoftheavianconecell 69 5.5. Summaryandoutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6. Discussions 75 7. Supplementary Material 91 8. Erklärung 115

[pt] Após uma criteriosa revisão de trabalhos acadêmicos que aplicam a abordagem de opções reais para a avaliação de concessões de infraestrutura e identificação das principais lacunas dessa literatura, desenvolvemos esta Tese, composta por quatro estudos independentes. O primeiro explica o modelo binomial e mostra como incorporar os fluxos de caixa do projeto usando a taxa de dividendos para criar a treliça de valor do projeto. Desenvolvemos um código em R, fornecemos um tutorial sobre este modelo e mostramos como o código pode ser personalizado para aplicações específicas. O segundo mostra porque cláusulas obrigatórias de investimentos adicionais em contratos de concessão são subótimos e propõe um modelo de opções reais que combina decisões flexíveis de expansão de capacidade com extensões condicionais de prazo. Usando um projeto de rodovia no Brasil, mostramos como essa flexibilidade pode ser útil para atrair investimentos privados em projetos públicos de infraestrutura. O terceiro avalia a concessão de um Veículo Leve sobre Trilhos no Brasil. Adotamos a abordagem de opções reais para modelar as cláusulas flexíveis embutidas neste contrato e analisamos se elas são conflitantes entre si e como impactam a avaliação geral do projeto. Por fim, o quarto utiliza testes de Raiz Unitária, Razão de Variância e Medida de Abordagem de Parâmetros para avaliar o processo estocástico mais adequado para modelar a incerteza de demanda de passageiros em concessões aeroportuárias no Brasil. Analisamos amostras ex-ante e ex-post covid-19 e mostramos que tanto a sazonalidade quanto a pandemia impactam significativamente o modelo de difusão estocástica. / [en] After a careful review of academic works that apply the real options approach to the evaluation of infrastructure concession projects and identifying the main gaps in this literature, we developed this Thesis, composed of four independent studies. The first explains the binomial model and shows how to incorporate the project cash flows using the cash flow dividend rate to create the project value lattice. We develop a R code, provide a tutorial on how to use this model and show how the code can be customized for particular applications. The second shows why additional investments in expansion as firm obligations in concession contracts are suboptimal and proposes a real options model that combines flexible capacity expansion decisions with conditional term extensions. Using a typical toll road project in Brazil, we show how this kind of flexibility can be useful for policy development to attract private investment in public infrastructure projects. The third evaluates the concession of a Light Rail Vehicle in Brazil. We adopt the real options approach to model the different flexible clauses embedded in this contract and analyze whether they conflict with each other and how they impact the overall project evaluation. Finally, the fourth uses Unit Root, Variance Ratio tests, and the Parameter Approach Measure to evaluate the most appropriate stochastic process to model the uncertainty of passenger demand in airport concessions in Brazil. We analyze samples ex-ante and ex-post covid-19 and show that both seasonality and the pandemic significantly impact the stochastic diffusion model.

With an increasing demand for bandwidth and lower latency in mobile communication networks it becomes gradually more important to improve current mobile network management solutions using available network data. To improve the network management it can for instance be of interest to infer future available bandwidth to the end user of the network. This can be done by utilizing the current knowledge of real-time user equipment (UE) behaviour in the network. In the scope of this thesis interest lies in, given a set of visited radio access points (cells), to predict what the next one is going to be. For this reason the aim is to investigate the prediction performance when utilizing the All-K-Order Markov (AKOM) model, with some added variations, on collected data generated from train trajectories. Moreover a method for testing the suitability of modeling the sequence of cells as a time-homogeneous Markov chain is proposed, in order to determine the goodness-of- t with the available data. Lastly, the elapsed time in each cell is attempted to be predicted using linear regression given the prior history window of previous cell and elapsed times pairs. The results show that moderate to good prediction accuracy on the upcoming cell can be achieved with AKOM and associated variations. For predicting the upcoming sojourn time in future cells the results reveal that linear regression does not yield satisfactory results and possibly another regression model should be utilized. / Med en ökande efterfrågan på banbredd och kortare latens i mobila nätverk har det gradvis blivit viktigare att förbättra nuvarande lösningar för hantering av nätverk genom att använda tillgänglig nätverksdata. Specifikt är det av intresse att kunna dra slutsatser kring vad framtida bandbredsförhållanden kommer vara, samt övriga parametrar av intresse genom att använda tillgänglig information om aktuell mobil användarutrustnings (UE) beteende i det mobila nätverket. Inom ramen av detta masterarbete ligger fokus på att, givet tidigare besökta radio accesspunkter (celler), kunna förutspå vilken nästkommande besökta cell kommer att vara. Av denna anledning är målet att undersöka vilken prestanda som kan uppnås när All-$K$-Order Markov (AKOM) modellen, med associerade varianter av denna, används på samlad data från tågfärder. Dessutom ges det förslag på test som avgör hur lämpligt det är att modelera observerade sekvenser av celler som en homogen Markovkedja med tillgänglig data. Slutligen undersöks även om besökstiden i en framtida cell kan förutspås med linjär regression givet ett historiskt fönster av tidigare cell och besökstids par. Erhållna resultat visar att måttlig till bra prestanda kan uppnås när kommande celler förutspås med AKOM modellen och associerade variationer. För prediktering av besökstid i kommande cell med linjär regression erhålles det däremot inte tillfredsställande resultat, vilket tyder på att en alternativ regressionsmetod antagligen är bättre lämpad för denna data.

An investment in a private equity is any investment made in a financial asset that is not publicly traded. As such these assets are very difficult to value and also give rise to great difficulty when it comes to quantifying risk. In a typical private equity investment the investor commits a prespecified amount of capital to a fund, this capital will be called upon as needed by the fund and eventually capital will be returned to the investor by the fund as it starts to turn a profit. In this way a private equity investment can be boiled down to consist of two cash flows, the contributions to the fund and distributions from the fund to the investor. These cash flows are usually made within a prespecified time frame but at unspecified intervals and amounts. As an investor in a fund, carrying too little liquid assets when contributions are called upon will cause trouble, but carrying significantly more than needed is also not desirable as it represents a loss in potential revenue from having less capital in more profitable investments. The goal of this thesis was to attempt to find a way to reliably model these cash flows and to find a way to represent the results in a meaningful way for the benefit of the investor by constructing value at risk like risk measures for the necessary liquid capital to carry at a given time in case contributions are called upon. It was found that the distributions could be modelled very well with the chosen stochastic processes, both as it related to predicting the average path of the cash flows and as it relates to modelling the variability of them. Contrary to this it was found that the contributions could not be modelled very well. The reason for this was found to be an observed lag in the speed of contributions at the start of the funds lifetime, this lag was not taken into account when constructing the stochastic model and hence it produced simulated cash flows not in line with those used in the calibration. / En investering i private equity är en investering i en tillgång som inte är börsnoterade. På grund av detta är sådana tillgångar väldigt svåra att värdera och medför även store svårigheter när det kommer till att kvantifiera risk. I en typisk private equity investering so ingår en investerare i ett löfte att under en viss förbestämd tidsperiod bidra med en fixt mängd kapital till en private equity fond. Detta kapital kommer att gradvis kallas på av fonden vid behov för att sedan mot slutet av fondens livstid ge utdelning när private equity fonden börjar göra en vinst. På detta viset kan en private equity investering brytas ner i två kassaflöden, kontributioner in i fonden, och distributioner ut ur fonden. Dessa kassaflöden sker under en förbestämd tidsperiod men ej förbestämda belopp. Som en investerare i denna typen av fond är därför en risk att bära för lite likvid kapital när kontributioner blir kallade på men även oattraktivt att bäre på för mycket de detta representerar förlorar potentiell avkastning. Målet i denna uppsatts är att hitta ett sätt att på att tillförlitligt vis modellera dessa kassaflöden och representera resultaten på ett meningsfullt sätt från perspektivet av en investerare. För att uppnå detta skapades value-at-risk liknande mått för mängden likvid kapital som krävs under en tidsperiod för att säkra sig mot påkallade kontributioner. Slutsatsen blev att distributioner kunde modelleras väl, både när det kom till att efterlikna den genomsnittliga vägen av kassaflöden och även för att modellera risken. I kontrast till detta så kunde inte kontributioner modelleras mot tillräckligt hög säkerhet för att användes i det ämnade syftena. Anledningen till detta var en eftersläpning i hastigheten som kontributioner kallades med som inte tågs i beaktande av den tillämpade matematiska modellen.

The liquidity of financial assets can be studied in various different ways. In this thesis, liquidity is defined as the cost and time required to liquidate a position. While the liquidity of highly traded financial instruments like stocks is typically determined by analyzing the order book, the lack of an order book for over-the-counter bond trading presents challenges for estimating bond liquidity. The objective of this thesis is to develop a framework for estimating the cost and time required to liquidate a bond position. To achieve this, we propose a theoretical order book model based on the order book of more actively traded instruments, and estimate the model parameters using bond transaction data. The volume available to trade in the theoretical order book was modelled as gamma distributed stochastic process. The distribution of the liquidation cost could thereafter be derived where the parameters were estimated using the maximum likelihood estimation. The liquidation time, or liquidity horizon, was then determined through the solution of an optimization problem. The proposed framework for estimating bond liquidity produced promising results. The estimated parameters of the gamma distributed stochastic process accurately captured the behavior of bond trading volumes, allowing for a reliable estimation of the distribution of liquidation costs. Additionally, the optimization problem used to determine the liquidity horizon produced reasonable estimates. / Likviditeten hos finansiella tillgångar kan studeras på olika sätt. I denna uppsats definieras likviditeten som kostnaden och tiden som krävs för att likvidera en position. Medans likviditeten hos aktivt handlade finansiella tillgångar som aktier vanligtvis bestäms genom att analysera orderboken, så medför bristen på en orderbok för handel med "over-the-counter" obligationer utmaningar för att uppskatta likviditeten för dem. Syftet med denna uppsats är att utveckla ett ramverk för att uppskatta kostnaden och tiden som krävs för att likvidera en obligationsposition. För att uppnå detta föreslår vi en teoretisk orderboksmodell baserad på orderboken för mer aktivt handlade instrument, och uppskattar modellparametrarna med hjälp av data för obligationsaffärer. Volymen som är tillgänglig att handla i den teoretiska orderboken modellerades som en gammafördelad stokastisk process. Fördelningen av likvidationskostnaden kunde sedan härledas där parametrarna uppskattades med hjälp av maximum likelihood-estimering. Likvidationstiden, eller likvidationshoristonten, bestämdes sedan genom att lösa ett optimeringsproblem. Det föreslagna ramverket för att uppskatta likviditeten hos obligationer gav lovande resultat. De uppskattade parametrarna för den gammafördelade stokastiska processen fångade noggrant upp beteendet hos handelsvolymerna för obligationer, vilket möjliggjorde en pålitlig uppskattning av fördelning av likvidationskostnader. Optimeringsproblemet som användes för att bestämma likviditetshorisontens gav dessutom rimliga uppskattningar.

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In this thesis, the credit worthiness of a company is modelled using a stochastic process. Two credit models are considered; Merton's model, which models the value of a firm's assets using geometric Brownian motion, and the distance to default model, which is driven by a two factor jump diffusion process. The probability of default and the default time are simulated using Monte Carlo and the number of scenarios needed to obtain convergence in the simulations is investigated. The simulations are performed using the probability matrix method (PMM), which means that a transition probability matrix describing the process is created and used for the simulations. Besides this, two variance reduction techniques are investigated; importance sampling and antithetic variates. / I den här uppsatsen modelleras kreditvärdigheten hos ett företag med hjälp av en stokastisk process. Två kreditmodeller betraktas; Merton's modell, som modellerar värdet av ett företags tillgångar med geometrisk Brownsk rörelse, och "distance to default", som drivs av en två-dimensionell stokastisk process med både diffusion och hopp. Sannolikheten för konkurs och den förväntade tidpunkten för konkurs simuleras med hjälp av Monte Carlo och antalet scenarion som behövs för konvergens i simuleringarna undersöks. Vid simuleringen används metoden "probability matrix method", där en övergångssannolikhetsmatris som beskriver processen används. Dessutom undersöks två metoder för variansreducering; viktad simulering (importance sampling) och antitetiska variabler (antithetic variates).

A stochastic operator is a positive linear contraction, P : L1 --+ L1, such that llPfII2 = llfll1 for f > 0. It is called asymptotically stable if the iterates pn f of each density converge in the norm to a fixed density. Pf(x) = f K(x,y)f(y)dy, where K( ·, y) is a density, defines a stochastic kernel operator. A general probabilistic/ deterministic model for biological systems is considered. This leads to the LMT operator P f(x) = Jo - Bx H(Q(>.(x)) - Q(y)) dy, where -H'(x) = h(x) is a density. Several particular examples of cell cycle models are examined. An operator overlaps supports iffor all densities f,g, pn f APng of 0 for some n. If the operator is partially kernel, has a positive invariant density and overlaps supports, it is asymptotically stable. It is found that if h( x) > 0 for x ~ xo ~ 0 and ["'" x"h(x) dx < liminf(Q(A(x))" - Q(x)") for a E (0, 1] lo x-oo then P is asymptotically stable, and an opposite condition implies P is sweeping. Many known results for cell cycle models follow from this. / Mathematical Science / M. Sc. (Mathematics)

Cette thèse s’intéresse à la gestion du risque climatique par l’utilisation des produits dérivés climatiques. Les travaux réalisés dans le cadre de cette thèse sont une contribution aux aspects statistiques, économétriques et financiers de la modélisation et de l'évaluation des produits dérivés climatiques. Un intérêt particulier a été accordé au contexte marocain aussi bien au niveau du volet qualitatif que quantitatif. En plus des développements théoriques que nous avons apportés (tests statistiques pour vérifier l’impact du climat sur l’économie, amélioration d’un modèle de prévision de la température moyenne quotidienne, confirmation du choix de la température moyenne, au lieu des températures extrêmes, comme sous-jacent pour les contrats basés sur la température, etc.), nous avons proposé des cas de gestion entre opérateurs économiques marocains exerçant des activités sensibles à l’aléa climatique avec des profils de risque différents en leur apportant des solutions de couverture basées sur l’utilisation de produits dérivés climatiques. / This thesis focuses on the weather risk management by using weather derivatives. The work done in this thesis is a contribution to statistics, econometric and financial aspects of the modeling and the evaluation of weather derivatives. Particular attention was paid to the Moroccan context both in a qualitative point of view. In additionto theoretical developments that we have made (statistical tests to verify the impact of weather conditions on the economy, improvement of a model to forecast daily average temperatures, confirming the choice of the average temperature instead of extreme temperatures as the preferred under lying for contracts based on temperature, etc.), we also proposed case studies with Moroccan economic actors carrying out their weather sensitive activities and having different risk profiles and we provide them hedging solutions based on the use of weather derivatives.