Magnetic resonance imaging (MRI) of the liver is an important non-invasive tool for diagnosing liver disease. A key application is dynamic contrast enhanced magnetic resonance imaging (DCE-MRI). With the use of the hepatocyte specific contrast agent (CA) Gd-EOB-DTPA it is now possible to evaluate the liver function. Beyond traditional qualitative evaluation of the DCE-MRI images, parametric quantitative techniques are on the rise which yields more objective evaluations. Systems biology is a gradually expanding field using mathematical modeling to gain deeper mechanistic understanding in complex biological systems. The aim of this thesis to combine these two fields in order to derive a physiologically accurate minimal whole body model that can be used to quantitatively evaluate liver function using clinical DCE-MRI examinations.  The work is based on two previously published sources of data using Gd-EOB-DTPA in healthy humans; i) a region of interest analysis of the liver using DCE-MRI ii) a pre-clinical evaluation of the contrast agent using blood sampling.  The modeling framework consists of a system of ordinary differential equations for the contrast agent dynamics and non-linear models for conversion of contrast agent concentrations to relaxivity values in the DCE-MRI image volumes. Using a χ2-test I have shown that the model, with high probability, can fit the experimental data for doses up to twenty times the clinically used one, using the same parameters for all doses. The results also show that some of the parameters governing the hepatocyte flux of CA can be numerically identifiable. Future applications with the model might be as a basis for regional liver function assessment. This can lead to disease diagnosis and progression evaluation for physicians as well as support for surgeons planning liver resection.

Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics of discrete fractional calculus are discussed using particular examples for further calculations. In Chapter 2, we use these basic results in the analysis of a linear fractional difference equation. Existence of solutions to this difference equation is then established for both initial conditions (IVP) and two-point boundary conditions (BVP). In Chapter 3, Green's functions are introduced and discussed, along with examples. Instead of using Cauchy functions, the technique of finding Green's functions by a traditional method is demonstrated and used throughout this chapter. The solutions of the BVP play an important role in analysis and construction of the Green's functions. Then, Green's functions for the discrete calculus case are calculated using particular problems, such as boundary value problems, discrete boundary value problems (DBVP) and fractional boundary value problems (FBVP). Finally, we demonstrate how the Green's functions of the FBVP generalize the existence results of the Green's functions of DVBP. In Chapter 4, different compartmental pharmacokinetic models are discussed. This thesis limits discussion to the one-compartmental model. The Mathematica FindFit command and the statistical computational techniques of mean square error (MSE) and cross-validation are discussed. Each of the four models (continuous, continuous fractional, discrete and discrete fractional) is used to compute the MSE numerically with the given data of drug concentration. Then, the best fit and the best model are obtained by inspection of the resulting MSE. In the last Chapter, the results are summarized, conclusions are drawn, and directions for future work are stated.

Le roman La ballade de Gilbert raconte l’histoire d’un homme dont la tranquille normalité du quotidien est perturbée lorsqu’il découvre qu’un de ses collègues de longue date fréquente des prostituées. Afin de retrouver son confort, il incite clandestinement ce collègue à se chercher une conjointe, mais cette quête devient peu à peu une profonde obsession qui bouleverse encore plus l’équilibre de sa vie routinière. À travers ce récit s’articule une réflexion sur le quotidien, sur les limites entre l’ordinaire et l’extraordinaire, le familier et l’étrange. L’essai Le quotidien dans Molloy de Samuel Beckett reprend le thème du quotidien afin d’analyser le dialogue entre le familier et l’étrangeté dans ce roman. Molloy présente de nombreux scénarios communs (Eco), qui correspondent très sensiblement d’un point de vue cognitif aux habitudes qui façonnent le quotidien d’un individu. Cet essai explique comment Beckett subvertit ces scénarios pour laisser place à une étrangeté derrière laquelle le familier demeure reconnaissable. / The novel La ballade de Gilbert tells the story of a man whose quiet and ordinary life is troubled when he realises that one of his long time colleagues is seeing prostitutes. To re-establish his comfort, he secretly tries to encourage this colleague to find a mate, but this quest becomes a relentless obsession that overturns even more the order of his life. A reflection about everyday life and the limits between the ordinary and the extraordinary, the familiar and the uncanny, is proposed through this narrative. The essay Le quotidien dans Molloy de Samuel Beckett also touches everyday life by the analysis of the dialogue between familiarity and strangeness. Molloy shows numerous examples of common scenarios (Eco), which correspond very closely, from the cognitive point of view, to the habits that shape an individual’s everyday life. This essay explains how Beckett subverts these scenarios to show a strangeness behind which familiarity remains visible.

Meningsfulla aktiviteter ingår i arbetsterapeutens kompetens och något som arbetsterapeuter bör grunda sina interventioner i. Syftet med examensarbetet var att beskriva upplevelse av möjlighet och hinder till meningsfulla aktiviteter hos äldre med hemtjänst i ordinärt boende. Examensarbetet hade en kvalitativ design med semistrukturerade intervjuer. Tio deltagare intervjuades. En kvalitativ innehålls-analys resulterade i faktorer som både möjliggjorde och hindrade meningsfulla aktiviteter. Tre kategorier identifierades; ”Den fysiska miljöns betydelse”, miljön kring den äldre påverkade utförandet beroende på om den var anpassad eller inte, om man hade närhet till aktivitet, om man hade möjlighet till transport samt att den varma årstiden möjliggjorde. ”Hindrande Personfaktorer”, kroppsliga begränsningar och mentala begränsningar påverkade möjlighet till utförande av meningsfulla aktiviteter. ”Organiserade sociala aktiviteter”, kyrkan möjliggjorde aktivitet, hemtjänsten stöttar till viss del och organiserade aktiviteter har lagts ned. Temat ”Det handlar inte om hur gammal man är, utan hur man är gammal” framkom. Samhällets syn på äldre samt äldres internaliserade syn på sig själva påverkar möjlighet till utförande av meningsfulla aktiviteter. Slutsatsen var att möjlighet till meningsfulla aktiviteter påverkas av omgivningsfaktorer och personfaktorer. Denna kunskap bidrar till att arbetsterapeuter kan arbeta för att äldre ska kunna utföra meningsfulla aktiviteter genom att uppmärksamma de hinder och möjligheter som den äldre upplever. / Meaningful occupations are part of the occupational therapist’s competence and should be the foundation in interventions. The aim was to describe the experience of the possibilities and hindrance to meaningful activities for elderly in ordinary living who has support from home care. The thesis had a qualitative design with semi structured interviews with ten participants. The result showed factors that enabled and disabled the possibility to perform meaningful activities. “The importance of the physical environment”, the environment around the elderly affected the performance due to if it was adapted or not. Activities nearby, transportation as well as light and warmth enabled meaningful activities. “Obstructive personal factors”, physical body factors and mental body factors affected the ability to perform meaningful activities. “Organized social activities”, the church enabled activities, the home care support to some extent and organizations have cancelled activities. The theme “It´s not about how old you are, but how you are old” emerged. Society’s opinion about the elderly and elder’s internalised opinion about themselves affect the possibility to meaningful activities. The conclusion showed that environmental factors and individual factors affected the ability to perform meaningful activities. This knowledge contributes to occupational therapists work to enable meaningful activities for the elderly.

Human induced pluripotent stem cells (hiPSCs) have two main properties: pluripotency and self-renewal. Physical cues presented by biomaterial scaffolds can stimulate differentiation of hiPSCs to neurons. In this work, we develop and analyze a mathematical model of aggregate growth and neural differentiation on melt electrospun biomaterial scaffolds. An ordinary differential equation model of population size of each cell state (stem, progenitor, differentiated) was developed based on experimental results and previous literature. Analysis and numerical simulations of the model successfully capture many of the dynamics observed experimentally. Analysis of the model gives optimal parameter sets, that correspond to experimental procedures, to maximize particular populations. The model indicates that a physiologic oxygen level (~5%) increases population sizes compared to atmospheric oxygen levels (~21%). Model analysis also indicates that the optimal scaffold porosity for maximizing aggregate size is approximately 63%. This model allows for the use of mathematical analysis and numerical simulations to determine the key factors controlling cell behavior when seeded on melt electrospun scaffolds. / Graduate

Ordinary differential equations (ODEs) play an important role in mathematics. Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are considered as maps from one function space to another, common numerical algorithms for ODEs discretise problems early on in the solution process. This thesis is about continuous analogues of such discrete algorithms for the numerical solution of ODEs. This thesis shows how Newton's method for finite dimensional system can be generalised to function spaces, where it is known as Newton-Kantorovich iteration. It presents affine invariant damping strategies for increasing the chance of convergence for the Newton-Kantorovich iteration. The derivatives required in this continuous setting are Fréchet derivatives, the continuous analogue of Jacobian matrices. In this work, we present how automatic differentiation techniques can be applied to compute Fréchet derivatives. We introduce chebop, a Matlab solver for nonlinear boundary-value problems, which combines damped Newton iteration in function space and automatic Fréchet differentiation. By proving that affine operators have constant Fréchet derivatives, it is demonstrated how automatic linearity detection of computed quantities can be implemented. This is valuable for black-box solvers, which can use the information to determine whether an iteration scheme has to be employed for solving a problem. Like nonlinear systems of equations, nonlinear boundary-value problems can have multiple solutions. This thesis present two techniques for obtaining multiple solutions of operator equations: deflation and path-following. An algorithm combining the two techniques is proposed.

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a set of time delays we hope to reconstruct attractors and identify members of these clusters.

The birth of complexity research derives from the logical progression of advancement in the scientific field afforded by reductionist theory. We present in silico models of two complex physiological processes, wound healing and coagulation/fibrinolysis based on two common tools in the study of complex physiology: ordinary differential equations (ODE) and Agent Based Modeling (ABM). The strengths of these two approaches are well-suited in the analysis of clinical paradigms such as wound healing and coagulation. The complex interactions that characterize acute wound healing have stymied the development of effective therapeutic modalities. The use of computational models holds the promise to improve our basic approach to understanding the process. We have modified an existing ordinary differential equation model by 1) evolving from a systemic model to a local model, 2) the incorporation of fibroblast activity, and3) including the effects of tissue oxygenation. Possible therapeutic targets, such as fibroblast death rate and rate of fibroblast recruitment have been identified by computational analysis. This model is a step toward constructing an integrative systems biology model of human wound healing. The coagulation and fibrinolytic systems are complex, inter-connected biological systems with major physiological roles. We present an Agent Based Modeling and Simulation (ABMS) approach to these complex interactions. This ABMS method successfully reproduces the initiation, propagation, and termination of blood clot formation and its lysis in vitro due to the activation of either the intrinsic or extrinsic pathways. Furthermore, the ABMS was able to simulate the pharmacological effects of two clinically used anticoagulants, warfarin and heparin, as well as the physiological effects of enzyme deficiency/dysfunction, i.e., hemophilia and antithrombin III-heparin binding impairment, on the coagulation system. The results of the model compare favorably with in vitro experimental data under both physiologic and pathophysiologic conditions. Our computational systems biology approach integrates reductionist experimental data into a cohesive model that allows rapid evaluation of the effects of multiple variables. Our ODE and AMBS models offer the ability to generate non-linear responses based on known relationships among variables and in silico modeling of mechanistic biological rules on computer software, respectively. Simulations of normal and disease states as well as effects of therapeutic intervention demonstrate the potential uses of computer simulation. Specifically, models may be applied to hypothesis generation and biological advances, discovery of new diagnostic and therapeutic options, platforms to test novel therapies, and opportunities to predict adverse events during drug development. The ultimate aim of such models is creation of bedside simulators that allow personalized, individual medicine; however, a myriad of opportunities for scientific advancement are opened through in silico experimentation.

The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.

Dans la résolution d’un conflit opérée conformément aux règles de droit qui lui sont applicables, les juridictions ordinaires françaises sont amenées à se prononcer sur l’applicabilité des normes conventionnelles au regard de leur conformité à la Constitution. Ce contrôle, longtemps cantonné à la seule vérification de l’existence de la procédure d’insertion de l’engagement international, s’est progressivement développé, jusqu’à conduire à une appréciation de la constitutionnalité externe de la norme internationale. Dans un contexte de prégnance exponentielle de l’ordre juridique international sur l’ordre juridique interne, cette dynamique jurisprudentielle est apparue comme un palliatif aux carences inhérentes au contrôle a priori pratiqué par le Conseil constitutionnel, interprète authentique et premier de la Constitution. La conjugaison des deux modes de contrôle de constitutionnalité, augmentée de l’examen préventif opéré par les formations administratives du Conseil d'État, n’apporte pourtant pas une réponse pleinement satisfaisante à l’ « angle mort » persistant dans le contrôle de constitutionnalité des normes internationales. En l’absence de titre d’habilitation au bénéfice du juge ordinaire dirigé contre elle, la norme internationale jouit d’une injusticiabilité de nature à obérer la suprématie de la Constitution dans l’ordre juridique interne. Le Conseil d'État et la Cour de cassation ont pourtant consacré cette supériorité. Mais le refus par le juge ordinaire d’étendre sa jurisprudence au contrôle de la constitutionnalité interne de la norme internationale rend inconséquente cette affirmation jurisprudentielle. L’instauration de la question prioritaire de constitutionnalité, loin de vider le débat de son intérêt, réactive les interrogations soulevées par l’appréhension des rapports de systèmes, en soulignant la nécessité d’opposer un contrôle de l’applicabilité des engagements internationaux en vigueur. Il convient dès lors de s’interroger sur la possibilité et sur l’opportunité d’une évolution en ce sens de la jurisprudence du Conseil d'État et de la Cour de cassation. L’enjeu de la réflexion menée n’est pas uniquement théorique. Au-delà des implications procédurales, elle dessine en creux les contours de la souveraineté nationale et interroge quant à sa réalité / In order to decide a case in accordance with applicable law, French ordinary jurisdictions are lead to determine whether applicable international rules comply with the Constitution. This supervision was long limited to the review of the insertion modalities of international treaties into domestic law and has progressively extended to the review of the external constitutionality of international rules. This evolution has compensated for the inherent shortcomings of the a priori review of international treaties carried out by the Constitutional Council, the final interpret of the Constitution. The conjugation of these two review mechanisms does not however satisfactorily address a “blind spot” in the area of the compliance of international rules to the Constitution. The fact that there are cases in which international rules cannot be reviewed jeopardizes the supremacy of the Constitution in domestic law. The Council of State and the Court of Cassation have however recognized this superiority but the refusal by ordinary jurisdictions to review the internal constitutionality of the international rules makes this superiority ineffective. The introduction of the “priority preliminary ruling on the issue of constitutionality revives the debate regarding systems relationships, and emphasizes the necessity of establishing a more complete review of the applicability of international treaties in force. Thoughts should be given to the possibility of such an evolution in the Council of State and Cassation Courts rulings. The stakes of the analysis here conducted are not only theoretical. Beyond procedural consequences, it draws a first outline of the national sovereignty, and questions as its reality