La question du développement inclusif dans les pays en développement est au cœur de cette thèse. Cette dernière s'articule autour de quatre chapitres sur les questions de politique fiscale et les questions liées à la croissance inclusive. Le chapitre 1 explore comment la politique fiscale de l’Etat affecte l'inclusivité de la croissance dans les pays en développement. Nous observons que la politique fiscale affecte la croissance inclusive de manière significative si et seulement si les pays ont de fortes qualités institutionnelles. En outre, notre résultat montre qu'il existe un seuil optimal au-delà duquel toute augmentation du taux d'imposition négativement la croissance inclusive. Le chapitre 2 examine les effets des composantes des dépenses publiques sur l'équité et la croissance dans les pays d’Afrique subsaharienne, notamment s'il est possible de concevoir des dépenses publiques en vue de promouvoir une société plus équitable sans sacrifier la croissance économique. Notre étude a permis de montrer que l’investissement en infrastructure a contribué à une croissance plus inclusive en Afrique subsaharienne que d'autres dépenses publiques. Ces résultats suggèrent que des programmes temporaires et bien ciblés devraient être mis en place pour aider ceux qui sont laissés pour compte par le processus de croissance. Le chapitre 3 cherche à savoir si les problèmes d’inégalités de revenus se sont posés ou non dans les périodes d'ajustement budgétaire en Côte d'Ivoire au cours de la période 1980-2014. Nos résultats montrent une amélioration de la performance de croissance après les épisodes de consolidation budgétaire, mais aussi des diminutions de l'écart de revenu dans les périodes suivantes les années d’ajustements budgétaires. Enfin, le chapitre 4 évalue la crédibilité des prévisions budgétaires et leurs effets sur le bien-être social dans les pays de la CEMAC et de l'UEMOA. Nous sommes aboutis aux résultats que l'inefficacité des prévisions budgétaires se produit dans la plupart des cas parce que les erreurs de prévisions sont proportionnelles à la prévision elle-même, mais aussi parce que les erreurs passées sont répétées dans le temps. En outre, une partie des erreurs de prévision des recettes peut s'expliquer par des chocs aléatoires survenus dans l'économie. Par conséquent, ces erreurs dans les prévisions de revenus considérées comme des chocs de politique budgétaire ont un effet négatif sur la croissance inclusive. / The issue of inclusive development in developing countries is at the heart of this thesis. The latter revolves around four chapters on fiscal policy issues and inclusive growth-related matters. Chapter 1 explores how government tax policy affects the inclusiveness of growth in developing countries. Evidence is shown that tax policy affects significantly inclusive growth if and only if the countries have a strong institution quality like low corruption and a good bureaucratic policy. In addition, our result shows that there is an optimal tax beyond which, any increase in the personal income tax rate should have negative impact on inclusive growth. The Chapter 2 examines the effects of government expenditure components on both equity and growth in sub-Saharan countries, especially whether it is possible to design public spending to promote a more equitable society without sacrificing economic growth. We find that investment in infrastructure contributed to more inclusive growth in Sub-sub Saharan African economies than others government spending. These results suggest that temporary and well-targeted programs should be implemented to help those being left out by the growth process. The Chapter 3 investigates whether income inequality matters in the periods of fiscal adjustments in Côte d’Ivoire over the period 1980-2014. The results show an improvement in growth performance after fiscal consolidations episodes, but also income gap decreases in the periods ahead fiscal adjustments. Lastly, Chapter 4 assesses the credibility of fiscal forecasts and their social effects in CEMAC and WAEMU countries. We obtain evidence that the inefficiency of fiscal forecast occurs in most time because the forecast deviation is proportional to the forecast itself, but also because the past errors are repeated in the present. Furthermore, a part of revenue forecast errors can be explained by random shocks to the economy. Therefore, these errors in revenue forecast considered as fiscal policy shocks has a detrimental effect on inclusive growth.

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De multiples problèmes en apprentissage automatique consistent à minimiser une fonction lisse sur un espace euclidien. Pour l’apprentissage supervisé, cela inclut les régressions par moindres carrés et logistique. Si les problèmes de petite taille sont résolus efficacement avec de nombreux algorithmes d’optimisation, les problèmes de grande échelle nécessitent en revanche des méthodes du premier ordre issues de la descente de gradient. Dans ce manuscrit, nous considérons le cas particulier de la perte quadratique. Dans une première partie, nous nous proposons de la minimiser grâce à un oracle stochastique. Dans une seconde partie, nous considérons deux de ses applications à l’apprentissage automatique : au partitionnement de données et à l’estimation sous contrainte de forme. La première contribution est un cadre unifié pour l’optimisation de fonctions quadratiques non-fortement convexes. Celui-ci comprend la descente de gradient accélérée et la descente de gradient moyennée. Ce nouveau cadre suggère un algorithme alternatif qui combine les aspects positifs du moyennage et de l’accélération. La deuxième contribution est d’obtenir le taux optimal d’erreur de prédiction pour la régression par moindres carrés en fonction de la dépendance au bruit du problème et à l’oubli des conditions initiales. Notre nouvel algorithme est issu de la descente de gradient accélérée et moyennée. La troisième contribution traite de la minimisation de fonctions composites, somme de l’espérance de fonctions quadratiques et d’une régularisation convexe. Nous étendons les résultats existants pour les moindres carrés à toute régularisation et aux différentes géométries induites par une divergence de Bregman. Dans une quatrième contribution, nous considérons le problème du partitionnement discriminatif. Nous proposons sa première analyse théorique, une extension parcimonieuse, son extension au cas multi-labels et un nouvel algorithme ayant une meilleure complexité que les méthodes existantes. La dernière contribution de cette thèse considère le problème de la sériation. Nous adoptons une approche statistique où la matrice est observée avec du bruit et nous étudions les taux d’estimation minimax. Nous proposons aussi un estimateur computationellement efficace. / Many problems in machine learning are naturally cast as the minimization of a smooth function defined on a Euclidean space. For supervised learning, this includes least-squares regression and logistic regression. While small problems are efficiently solved by classical optimization algorithms, large-scale problems are typically solved with first-order techniques based on gradient descent. In this manuscript, we consider the particular case of the quadratic loss. In the first part, we are interestedin its minimization when its gradients are only accessible through a stochastic oracle. In the second part, we consider two applications of the quadratic loss in machine learning: clustering and estimation with shape constraints. In the first main contribution, we provided a unified framework for optimizing non-strongly convex quadratic functions, which encompasses accelerated gradient descent and averaged gradient descent. This new framework suggests an alternative algorithm that exhibits the positive behavior of both averaging and acceleration. The second main contribution aims at obtaining the optimal prediction error rates for least-squares regression, both in terms of dependence on the noise of the problem and of forgetting the initial conditions. Our new algorithm rests upon averaged accelerated gradient descent. The third main contribution deals with minimization of composite objective functions composed of the expectation of quadratic functions and a convex function. Weextend earlier results on least-squares regression to any regularizer and any geometry represented by a Bregman divergence. As a fourth contribution, we consider the the discriminative clustering framework. We propose its first theoretical analysis, a novel sparse extension, a natural extension for the multi-label scenario and an efficient iterative algorithm with better running-time complexity than existing methods. The fifth main contribution deals with the seriation problem. We propose a statistical approach to this problem where the matrix is observed with noise and study the corresponding minimax rate of estimation. We also suggest a computationally efficient estimator whose performance is studied both theoretically and experimentally.

Pharmacometrics is widely used in drug development. Models are developed to describe pharmacological measurements with data gathered from a clinical trial. The information can then be applied to, for instance, safely establish dose-response relationships of a substance. Glycated hemoglobin (HbA1c) is a common biomarker used by models within antihyperglycemic drug development, as it reflects the average plasma glucose level over the previous 8-12 weeks. There are five different nonlinear mixed-effects models that describes HbA1c-formation. They use different biomarkers such as mean plasma glucose (MPG), fasting plasma glucose (FPG), fasting plasma insulin (FPI) or a combination of those. The aim of this study was to compare their performances on a population and an individual level using model averaging (MA) and to explore if reduced trial durations and different treatment could affect the outcome. Multiple weighting methods were applied to the MA workflow, such as the Akaike information criterion (AIC), cross-validation (CV) and a bootstrap model averaging method. Results show that in general, models that use MPG to describe HbA1c-formation on a population level could potentially outperform models using other biomarkers, however, models have shown similar performance on individual level. Further studies on the relationship between biomarkers and model performances must be conducted, since it could potentially lay the ground for better individual HbA1c-predictions. It can then be applied in antihyperglycemic drug development and to possibly reduce sample sizes in a clinical trial. With this project, we have illustrated how to perform MA on the aforementioned models, using different biomarkers as well as the difference between model weights on a population and individual level.

Die vorliegende Arbeit behandelt die kollektive Dynamik identischer Klasse-I-anregbarer Elemente. Diese können im Rahmen der nichtlinearen Dynamik als Systeme nahe einer Sattel-Knoten-Bifurkation auf einem invarianten Kreis beschrieben werden. Der Fokus der Arbeit liegt auf dem Studium aktiver Rotatoren als Prototypen solcher Elemente. In Teil eins der Arbeit besprechen wir das klassische Modell abstoßend gekoppelter aktiver Rotatoren von Shinomoto und Kuramoto und generalisieren es indem wir höhere Fourier-Moden in der internen Dynamik der Rotatoren berücksichtigen. Wir besprechen außerdem die mathematischen Methoden die wir zur Untersuchung des Aktive-Rotatoren-Modells verwenden. In Teil zwei untersuchen wir Existenz und Stabilität periodischer Zwei-Cluster-Lösungen für generalisierte aktive Rotatoren und beweisen anschließend die Existenz eines Kontinuums periodischer Lösungen für eine Klasse Watanabe-Strogatz-integrabler Systeme zu denen insbesondere das klassische Aktive-Rotatoren-Modell gehört und zeigen dass (i) das Kontinuum eine normal-anziehende invariante Mannigfaltigkeit bildet und (ii) eine der auftretenden periodischen Lösungen Splay-State-Dynamik besitzt. Danach entwickeln wir mit Hilfe der Averaging-Methode eine Störungstheorie für solche Systeme. Mit dieser können wir Rückschlüsse auf die asymptotische Dynamik des generalisierten Aktive-Rotatoren-Modells ziehen. Als Hauptergebnis stellen wir fest dass sowohl periodische Zwei-Cluster-Lösungen als auch Splay States robuste Lösungen für das Aktive-Rotatoren-Modell darstellen. Wir untersuchen außerdem einen "Stabilitätstransfer" zwischen diesen Lösungen durch sogenannte Broken-Symmetry States. In Teil drei untersuchen wir Ensembles gekoppelter Morris-Lecar-Neuronen und stellen fest, dass deren asymptotische Dynamik der der aktiven Rotatoren vergleichbar ist was nahelegt dass die Ergebnisse aus Teil zwei ein qualitatives Bild für solch kompliziertere und realistischere Neuronenmodelle liefern. / We study the collective dynamics of class I excitable elements, which can be described within the theory of nonlinear dynamics as systems close to a saddle-node bifurcation on an invariant circle. The focus of the thesis lies on the study of active rotators as a prototype for such elements. In part one of the thesis, we motivate the classic model of repulsively coupled active rotators by Shinomoto and Kuramoto and generalize it by considering higher-order Fourier modes in the on-site dynamics of the rotators. We also discuss the mathematical methods which our work relies on, in particular the concept of Watanabe-Strogatz (WS) integrability which allows to describe systems of identical angular variables in terms of Möbius transformations. In part two, we investigate the existence and stability of periodic two-cluster states for generalized active rotators and prove the existence of a continuum of periodic orbits for a class of WS-integrable systems which includes, in particular, the classic active rotator model. We show that (i) this continuum constitutes a normally attracting invariant manifold and that (ii) one of the solutions yields splay state dynamics. We then develop a perturbation theory for such systems, based on the averaging method. By this approach, we can deduce the asymptotic dynamics of the generalized active rotator model. As a main result, we find that periodic two-cluster states and splay states are robust periodic solutions for systems of identical active rotators. We also investigate a 'transfer of stability' between these solutions by means of so-called broken-symmetry states. In part three, we study ensembles of higher-dimensional class I excitable elements in the form of Morris-Lecar neurons and find the asymptotic dynamics of such systems to be similar to those of active rotators, which suggests that our results from part two yield a suitable qualitative description for more complicated and realistic neural models.

There exists substantial applications motivating the study of nonlinear longitudinal wave propagation in layered (or laminated) elastic waveguides, in particular within areas related to non-destructive testing, where there is a demand to understand, reinforce, and improve deformation properties of such structures. It has been shown [76] that long longitudinal waves in such structures can be accurately modelled by coupled regularised Boussinesq (cRB) equations, provided the bonding between layers is sufficiently soft. The work in this thesis firstly examines the initial-value problem (IVP) for the system of cRB equations in [76] on the infinite line, for localised or sufficiently rapidly decaying initial conditions. Using asymptotic multiple-scales expansions, a nonsecular weakly nonlinear solution of the IVP is constructed, up to the accuracy of the problem formulation. The asymptotic theory is supported with numerical simulations of the cRB equations. The weakly nonlinear solution for the equivalent IVP for a single regularised Boussinesq equation is then constructed; constituting an extension of the classical d'Alembert's formula for the leading order wave equation. The initial conditions are also extended to allow one to separately specify an O(1) and O(ε) part. Large classes of solutions are derived and several particular examples are explicitly analysed with numerical simulations. The weakly nonlinear solution is then improved by considering the IVP for a single regularised Boussinesq-type equation, in order to further develop the higher order terms in the solution. More specifically, it enables one to now correctly specify the higher order term's time dependence. Numerical simulations of the IVP are compared with several examples to justify the improvement of the solution. Finally an asymptotic procedure is developed to describe the class of radiating solitary wave solutions which exist as solutions to cRB equations under particular regimes of the parameters. The validity of the analytical solution is examined with numerical simulations of the cRB equations. Numerical simulations throughout this work are derived and implemented via developments of several finite difference schemes and pseudo-spectral methods, explained in detail in the appendices.

This thesis consists of three chapters on economic and econometric applications of Bayesian parameter estimation and model comparison. The first two chapters study the incidental parameter problem mainly under a linear autoregressive (AR) panel data model with fixed effect. The first chapter investigates the problem from a model comparison perspective. The major finding in the first chapter is that consistency in parameter estimation and model selection are interrelated. The reparameterization of the fixed effect parameter proposed by Lancaster (2002) may not provide a valid solution to the incidental parameter problem if the wrong set of exogenous regressors are included. To estimate the model consistently and to measure its goodness of fit, the Bayes factor is found to be more preferable for model comparson than the Bayesian information criterion based on the biased maximum likelihood estimates. When the model uncertainty is substantial, Bayesian model averaging is recommended. The method is applied to study the relationship between financial development and economic growth. The second chapter proposes a correction function approach to solve the incidental parameter problem. It is discovered that the correction function exists for the linear AR panel model of order p when the model is stationary with strictly exogenous regressors. MCMC algorithms are developed for parameter estimation and to calculate the Bayes factor for model comparison. The last chapter studies how stock return's predictability and model uncertainty affect a rational buy-and-hold investor's decision to allocate her wealth for different lengths of investment horizons in the UK market. The FTSE All-Share Index is treated as the risky asset, and the UK Treasury bill as the riskless asset in forming the investor's portfolio. Bayesian methods are employed to identify the most powerful predictors by accounting for model uncertainty. It is found that though stock return predictability is weak, it can still affect the investor's optimal portfolio decisions over different investment horizons.

Les conséquences liées à la présence de gradients thermiques sur le transfert de matière en milieu poreux sont encore aujourd’hui mal appréhendées, essentiellement en raison de la complexité induite par la présence de phénomènes couplés (thermodiffusion ou effet Soret). Le but de cette thèse est d’étudier et de comprendre l’influence que peut avoir un gradient thermique sur l’écoulement d’un mélange. L’objectif principal est de déterminer les coefficients effectifs modélisant les transferts de chaleur et de matière en milieux poreux, et en particulier le coefficient de thermodiffusion effectif. En utilisant la technique de changement d’échelle par prise de moyenne volumique nous avons développé un modèle macroscopique de dispersion incluant la thermodiffusion. Nous avons étudié en particulier l'influence du nombre de Péclet et de la conductivité thermique sur la thermodiffusion. Les résultats ont montré que pour de faibles nombres de Péclet, le nombre de Soret effectif en milieu poreux est le même que dans un milieu libre, et ne dépend pas du ratio de la conductivité thermique (solide/liquide). À l'inverse, en régime convectif, le nombre de Soret effectif diminue. Dans ce cas, un changement du ratio de conductivité changera le coefficient de thermodiffusion effectif. Les résultats théoriques ont montré également que, lors de la diffusion pure, même si la conductivité thermique effective dépend de la connectivité de la phase solide, le coefficient effectif de thermodiffusion est toujours constant et indépendant de la connectivité de la phase solide. Le modèle macroscopique obtenu par cette méthode est validé par comparaison avec des simulations numériques directes à l'échelle des pores. Un bon accord est observé entre les prédictions théoriques provenant de l'étude à l’échelle macroscopique et des simulations numériques au niveau de l’échelle de pores. Ceci démontre la validité du modèle théorique proposé. Pour vérifier et consolider ces résultats, un dispositif expérimental a été réalisé pour mesurer les coefficients de transfert en milieu libre et en milieu poreux. Dans cette partie, les nouveaux résultats expérimentaux sont obtenus avec un système du type « Two-Bulb apparatus ». La diffusion et la thermodiffusion des systèmes binaire hélium-azote et hélium-dioxide de carbone, à travers des échantillons cylindriques remplis de billes de différents diamètres et propriétés thermiques, sont mesurées à la pression atmosphérique. La porosité de chaque milieu a été déterminée par la construction d'une image 3D de l'échantillon par tomographie. Les concentrations sont déterminées par l'analyse en continu de la composition du mélange de gaz dans les ampoules à l’aide d’un catharomètre. La détermination des coefficients de diffusion et de thermodiffusion est réalisée par confrontation des relevés temporels des concentrations avec une solution analytique modélisant le transfert de matière entre deux ampoules. Les résultats sont en accord avec les résultats théoriques. Cela permet de conforter l’influence de la porosité des milieux poreux sur les mécanismes de diffusion et de thermodiffusion. / A multicomponent system, under nonisothermal condition, shows mass transfer with cross effects described by the thermodynamics of irreversible processes. The flow dynamics and convective patterns in mixtures are more complex than those of one-component fluids due to interplay between advection and mixing, solute diffusion, and thermal diffusion (or Soret effect). This can modify species concentrations of fluids crossing through a porous medium and leads to local accumulations. There are many important processes in nature and industry where thermal diffusion plays a crucial role. Thermal diffusion has various technical applications, such as isotope separation in liquid and gaseous mixtures, identification and separation of crude oil components, coating of metallic parts, etc. In porous media, the direct resolution of the convection-diffusion equations are practically impossible due to the complexity of the geometry; therefore the equations describing average concentrations, temperatures and velocities must be developed. They might be obtained using an up-scaling method, in which the complicated local situation (transport of energy by convection and diffusion at pore scale) is described at the macroscopic scale. At this level, heat and mass transfers can be characterized by effective tensors. The aim of this thesis is to study and understand the influence that can have a temperature gradient on the flow of a mixture. The main objective is to determine the effective coefficients modelling the heat and mass transfer in porous media, in particular the effective coefficient of thermodiffusion. To achieve this objective, we have used the volume averaging method to obtain the modelling equations that describes diffusion and thermodiffusion processes in a homogeneous porous medium. These results allow characterising the modifications induced by the thermodiffusion on mass transfer and the influence of the porous matrix properties on the thermodiffusion process. The obtained results show that the values of these coefficients in porous media are completely different from the one of the fluid mixture, and should be measured in realistic conditions, or evaluated with the theoretical technique developed in this study. Particularly, for low Péclet number (diffusive regime) the ratios of effective diffusion and thermodiffusion to their molecular coefficients are almost constant and equal to the inverse of the tortuosity coefficient of the porous matrix, while the effective thermal conductivity is varying by changing the solid conductivity. In the opposite, for high Péclet numbers (convective regime), the above mentioned ratios increase following a power law trend, and the effective thermodiffusion coefficient decreases. In this case, changing the solid thermal conductivity also changes the value of the effective thermodiffusion and thermal conductivity coefficients. Theoretical results showed also that, for pure diffusion, even if the effective thermal conductivity depends on the particle-particle contact, the effective thermal diffusion coefficient is always constant and independent of the connectivity of the solid phase. In order to validate the theory developed by the up-scaling technique, we have compared the results obtained from the homogenised model with a direct numerical simulation at the microscopic scale. These two problems have been solved using COMSOL Multiphysics, a commercial finite elements code. The results of comparison for different parameters show an excellent agreement between theoretical and numerical models. In all cases, the structure of the porous medium and the dynamics of the fluid have to be taken into account for the characterization of the mass transfer due to thermodiffusion. This is of great importance in the concentration evaluation in the porous medium, like in oil reservoirs, problems of pollution storages and soil pollution transport. Then to consolidate these theoretical results, new experimental results have been obtained with a two-bulb apparatus are presented. The diffusion and thermal diffusion of a helium-nitrogen and helium-carbon dioxide systems through cylindrical samples filled with spheres of different diameters and thermal properties have been measured at the atmospheric pressure. The porosity of each medium has been determined by construction of a 3D image of the sample made with an X-ray tomograph device. Concentrations are determined by a continuous analysing the gas mixture composition in the bulbs with a katharometer device. A transient-state method for coupled evaluation of thermal diffusion and Fick coefficients in two bulbs system has been proposed. The determination of diffusion and thermal diffusion coefficients is done by comparing the temporal experimental results with an analytical solution modelling the mass transfer between two bulbs. The results are in good agreement with theoretical results and emphasize the porosity of the medium influence on both diffusion and thermal diffusion process. The results also showed that the effective thermal diffusion coefficients are independent from thermal conductivity ratio and particle-particle touching.

This work is devoted to investigating the algebraic and analytic integrability of first order polynomial partial differential equations via an understanding of the well-developed area of local and global integrability of polynomial vector fields. In the view of characteristics method, the search of first integrals of the first order partial differential equations P(x,y,z)∂z(x,y) ∂x +Q(x,y,z)∂z(x,y) ∂y = R(x,y,z), (1) is equivalent to the search of first integrals of the system of the ordinary differential equations dx/dt= P(x,y,z), dy/dt= Q(x,y,z), dz/dt= R(x,y,z). (2) The trajectories of (2) will be found by representing these trajectories as the intersection of level surfaces of first integrals of (1). We would like to investigate the integrability of the partial differential equation (1) around a singularity. This is a case where understanding of ordinary differential equations will help understanding of partial differential equations. Clearly, first integrals of the partial differential equation (1), are first integrals of the ordinary differential equations (2). So, if (2) has two first integrals φ1(x,y,z) =C1and φ2(x,y,z) =C2, where C1and C2 are constants, then the general solution of (1) is F(φ1,φ2) = 0, where F is an arbitrary function of φ1and φ2. We choose for our investigation a system with quadratic nonlinearities and such that the axes planes are invariant for the characteristics: this gives three dimensional Lotka– Volterra systems x' =dx/dt= P = x(λ +ax+by+cz), y' =dy/dt= Q = y(µ +dx+ey+ fz), z' =dz/dt= R = z(ν +gx+hy+kz), where λ,µ,ν 6= 0. v Several problems have been investigated in this work such as the study of local integrability and linearizability of three dimensional Lotka–Volterra equations with (λ:µ:ν)–resonance. More precisely, we give a complete set of necessary and sufficient conditions for both integrability and linearizability for three dimensional Lotka-Volterra systems for (1:−1:1), (2:−1:1) and (1:−2:1)–resonance. To prove their sufficiency, we mainly use the method of Darboux with the existence of inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable. Also, more general three dimensional system have been investigated and necessary and sufficient conditions are obtained. In another approach, we also consider the applicability of an entirely different method which based on the monodromy method to prove the sufficiency of integrability of these systems. These investigations, in fact, mean that we generalized the classical centre-focus problem in two dimensional vector fields to three dimensional vector fields. In three dimensions, the possible mechanisms underling integrability are more difficult and computationally much harder. We also give a generalization of Singer’s theorem about the existence of Liouvillian first integrals in codimension 1 foliations in Cnas well as to three dimensional vector fields. Finally, we characterize the centres of the quasi-homogeneous planar polynomial differential systems of degree three. We show that at most one limit cycle can bifurcate from the periodic orbits of a centre of a cubic homogeneous polynomial system using the averaging theory of first order.

Poor drug penetration through tumor tissue has emerged as a fundamental obstacle to cancer therapy. The solid tumor microenvironment presents several physiological abnormalities which reduce the uptake of intravenously administered therapeutics, including leaky, irregularly spaced blood vessels, and a pressure gradient which resists transport of therapeutics from the bloodstream into the tumor. Because of these factors, a systemically administered anti-cancer agent is unlikely to reach 100% of cancer cells at therapeutic dosages, which is the efficacy required for curative treatment. The goal of this project is to use high-intensity focused ultrasound (HIFU) to enhance drug delivery via phenomena associated with acoustic cavitation. ‘Cavitation’ is the formation, oscillation, and collapse of bubbles in a sound field, and can be broadly divided into two types: ‘inertial’ and ‘stable’. Inertial cavitation involves violent bubble collapse and is associated with phenomena such as heating, fluid jetting, and broadband noise emission. Stable cavitation occurs at lower pressure amplitudes, and can generate liquid microstreaming in the bubble vicinity. It is the combination of fluid jetting and microstreaming which it is attempted to explore, control, and apply to the drug delivery problem in solid tumors. First, the potential for cavitation to enhance the convective transport of a model therapeutic into obstructed vasculature in a cell-free in vitro tumor model is evaluated. Transport is quantified using post-treatment image analysis of the distribution of a dye-labeled macromolecule, while cavitation activity is quantified by analyzing passively recorded acoustic emissions. The introduction of exogenous cavitation nuclei into the acoustic field is found to dramatically enhance both cavitation activity and convective transport. The strong correlation between inertial cavitation activity and drug delivery in this study suggested both a mechanism of action and the clinical potential for non-invasive treatment monitoring. Next, a flexible and efficient method to simulate numerically the microstreaming fields instigated by cavitating microbubbles is developed. The technique is applied to the problem of quantifying convective transport of a scalar quantity in the vicinity of acoustically cavitating microbubbles of various initial radii subject to a range of sonication parameters, yielding insight regarding treatment parameter choice. Finally, in vitro and in vivo models are used to explore the effect of HIFU on delivery and expression of a biologically active adenovirus. The role of cavitation in improving the distribution of adenovirus in porous media is established, as well as the critical role of certain sonication parameters in sustaining cavitation activity in vivo. It is shown that following intratumoral or intravenous co-injection of ultrasound contrast agents and adenovirus, both the distribution and expression of viral transgenes are enhanced in the presence of inertial cavitation. This ultrasound-based drug delivery system has the potential to be applied in conjunction with a broad range of macromolecular therapeutics to augment their bioavailability for cancer treatment. In order to reach this objective, further developmental work is recommended, directed towards improving therapeutic transducer design, using transducer arrays for treatment monitoring and mapping, and continuing the development of functionalized monodisperse cavitation nuclei.