Improving chemical transport models for atmospheric simulations relies on future developments of mathematical methods and parallelization methods. Better mathematical methods allow simulations to more accurately model realistic processes and/or to run in a shorter amount of time. Parellization methods allow simulations to run in much shorter amounts of time, therefore allowing scientists to use more accurate or more detailed simulations (higher resolution grids, smaller time steps). The state-of-the-science GEOS-Chem model is modified to use the Kinetic Pre-Processor, giving users access to an array of highly efficient numerical integration methods and to a wide variety of user options. Perl parsers are developed to interface GEOS-Chem with KPP in addition to modifications to KPP allowing KPP integrators to interface with GEOS-Chem. A variety of different numerical integrators are tested on GEOS-Chem, demonstrating that KPP provided chemical integrators produce more accurate solutions in a given amount of time than the original GEOS-Chem chemical integrator. The STEM chemical transport model provides a large scale end-to-end application to experiment with running chemical integration methods and transport methods on GPUs. GPUs provide high computational power at a fairly cheap cost. The CUDA programming environment simplifies the GPU development process by providing access to powerful functions to execute parallel code. This work demonstrates the accleration of a large scale end-to-end application on GPUs showing significant speedups. This is achieved by implementing all relevant kernels on the GPU using CUDA. Nevertheless, further improvements to GPUs are needed to allow these applications to fully exploit the power of GPUs. / Master of Science

Bakgrund: KPP står för Kostnad Per Patient, vilket är en kalkylmodell som gör det möjligt att redovisa kostnader för varje enskild patients vårdkontakt. Syftet med KPP är att bidra med information vilket möjliggör jämförelse och analys av den utförda hälso- och sjukvården. KPP-modellen har funnits sedan 80-talet, men ännu inte nått sin fulla potential, vi ansåg därför det intressant att studera användningen av KPP inom landstingen samt deras svårigheter och möjligheter. Syftet: Denna uppsats syftar till att kartlägga utbredningen och användningen av KPP i Sveriges landsting samt analysera de svårigheter och möjligheter som finns med användandet av KPP. Metod: Denna studie utgår från en tvärsnittsdesign med både kvantitativa och kvalitativa aspekter. Studiens insamlade empiri utgörs av telefonintervjuer med 15 KPP-kontaktpersoner ute i Sveriges landsting.  Kvantitativa delen redogör för KPP-användningsområden. I den kvalitativa delen analyseras svårigheter och möjligheter utifrån respondenternas perspektiv. Teoretisk referensram: Studiens teoretiska referensram består till stor del av KPP-modellen samt dess olika användningsområden inom ekonomistyrning. Vidare har vi redogjort för de relevanta ekonomistyrningsteorier som kan kopplas till KPP, vilket i grova drag är kalkylering, benchmarking samt verksamhetsuppföljning. Eftersom sjukvården är en komplex verksamhet behandlas slutligen svårigheter och problem, vilka kan uppstå i samband med ekonomistyrning inom sjukvården. Slutsats: Användningsområden för KPP är många och, största nyttan upplevs i benchmarking, kostnadsanalys samt verksamhetsuppföljning. Svårigheter med KPP-användandet hör av förklarliga skäl samman med tidpunkten vid införandet av KPP inom landstingen. För att överbygga svårigheter och problem, vilka upplevs idag ser vi att utveckling av det gemensamma språket mellan ekonomi och sjukvård är en nyckel till framgång. Genom att utveckla och förbättra arbetet med KPP kopplat till kvalitetsregister där kostnader knyts till uppnådd kvalitet skulle potentiellt bidra till ökad acceptans och användning av KPP inom verksamheten samt bidra till KPP-metodens framtida utveckling. / Background: KPP stands for cost per patient, which is a calculation method, enabling accounting for a specific patient´s contact in the healthcare. The purpose with KPP is to contribute with information, which enables comparison and analysis of the treatment given. The model of KPP has existed since the late 1980´s but hasn’t reached its full potential. Thus we found it interesting to analyse the use of KPP among the counties of Sweden, including the difficulties and possibilities related to KPP. Purpose: The purpose of this thesis is to map the spread and areas of use for KPP among the Swedish counties and to analyse the existing difficulties and possibilities related with the use of KPP. Method: This thesis proceeds from a cross-sectional study and includes both quantitative and qualitative aspects. The collected data of this thesis constitutes of telephone interviews with 15 persons in charge of KPP among the Swedish counties. The quantitative part of this thesis narrates the use of KPP. In the qualitative part analyses the difficulties and possibilities from the counties perspective. Theoretical framework: In this thesis the theoretical framework contains of the model of KPP as well as the it´s different areas of use related to management accounting. The theoretical framework also includes relevant theories connected to management accounting and the difficulties and complications related to management accounting in the healthcare sector. Conclusion: The areas of for KPP are many and the greatest utility is perceived to be benchmarking, cost analysis and monitoring activities. Difficulties with the use of KPP are for obvious reasons related to the time of implementation in the different counties. To overcome the difficulties perceived today we can conclude that the development of a mutual language between economy and healthcare is a key for success. By developing a connection between KPP and quality, where costs are connected to the quality in medical procedures, we see that KPP´s potential would reach higher levels. Thus it would contribute to an increase of acceptance and use of KPP among the healthcare sector, which also would gild the development of the KPP model in the future.

Cette thèse est consacrée à l'étude d'équations de réaction-diffusion de type KPP (Kolmogorov, Petrovsky et Piskunov) en milieu périodique. Ces équations servent de modèles notamment en combustion et en écologie. On s'intéresse plus particulièrement aux ondes pulsatoires et aux solutions proches de celles-ci, ainsi qu'à leurs propriétés qualitatives. La partie centrale de notre travail porte sur l'équation de type KPP en milieu périodique unidimensionnel $u_t - u_{xx}=f(x,u)$. Nous établissons tout d'abord l'existence d'ondes pulsatoires au comportement précisé à l'infini, ce qui permet d'exhiber ensuite des comportements non triviaux en temps grand. Nous terminons par l'étude du système de réaction-diffusion de la SHS (Self-propagating High-temperature Synthesis) en combustion solide, pour lequel nous montrons l'existence d'un continuum de vitesses donnant lieu à des ondes pulsatoires.

<p>Denna uppsats studerar universitetssjukhus implementering och användning av måttet KPP, kostnad per patient, inom den interna ekonomiska uppföljningen i somatisk slutenvård genom en intervju- och enkätundersökning.  Syftet är att se hur KPP bör implementeras och användas. Slutsatsen är att sjukhusens ledning inte fokuserats på den strategiska och operativa styrningen med hjälp av KPP, vilket försenat utbredningen av den interna användningen. KPP-måttet måste vara tillgängligt för alla nivåer inom sjukhuset och speciellt för verksamhetschefer med ansvar för vården av patienter; goda IT-system är också nödvändiga. Tiden sedan KPP införts har påverkat den interna användningen.</p>

Denna uppsats studerar universitetssjukhus implementering och användning av måttet KPP, kostnad per patient, inom den interna ekonomiska uppföljningen i somatisk slutenvård genom en intervju- och enkätundersökning.  Syftet är att se hur KPP bör implementeras och användas. Slutsatsen är att sjukhusens ledning inte fokuserats på den strategiska och operativa styrningen med hjälp av KPP, vilket försenat utbredningen av den interna användningen. KPP-måttet måste vara tillgängligt för alla nivåer inom sjukhuset och speciellt för verksamhetschefer med ansvar för vården av patienter; goda IT-system är också nödvändiga. Tiden sedan KPP införts har påverkat den interna användningen.

Statistical mechanics has been applied to a wide range of systems in physics, biology, medicine and even anthropology. This theory has been recently used to model the complex biochemical processes of gene expression and regulation. In particular, genetic networks offer a large number of interesting phenomena, such as multistability and oscillatory behaviour, that can be modelled with statistical mechanics tools. In the first part of this thesis we introduce gene regulation, genetic switches, and the colonization of a spatially structured media. We also introduce statistical mechanics and some of its useful tools, such as the master equation and mean- field theories. We present simple examples that are both pedagogical and also set the basis for the study of more complicated scenarios. In the second part we consider the exclusive genetic switch, a fundamental example of genetic networks. In this system, two proteins compete to regulate each other's dynamics. We characterize the switch by solving the stationary state in different limits of the protein binding and unbinding rates. We perform a study of the bistability of the system by examining its probability distribution, and by applying information theory techniques. We then present several versions of a mean field theory that offers further information about the switch. Finally, we compute the stationary probability distribution with an exact perturbative approach in the unbinding parameter, obtaining a valid result for a wide range of parameters values. The techniques used for this calculation are successfully applied to other switches. The topic studied in the third part of the thesis is the propagation of a trait inside an expanding population. This trait may represent resistance to an antibiotic or being infected with a certain virus. Although our model accounts for different examples in the genetic context, it is also very useful for the general study of a trait propagating in a population. We compute the speed of expansion and the stationary population densities for the invasion of an established and an expanding population, finding non-trivial criteria for speed selection and interesting speed transitions. The obtained formulae for the different wave speeds show excellent agreement with the results provided by simulations. Moreover, we are able to obtain the value of the speeds through a detailed analysis of the populations, and establish the requirements for our equations to present speed transitions. We finally apply our model to the propagation in a position-dependent fitness landscape. In this situation, the growth rate or the maximum concentration depends on the position. The amplitudes and speeds of the waves are again successfully predicted in every case.

In this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in \mathbb{R}\backslash\{0\}$. An important example, in the case when $k > 0$, is equations of the FKPP-type. We also give an example from the theory of utility maximisation problems when such equations arise and in this case $k < 0$. We introduce a new representation, for the solution of the equation, as the optimal value of an optimal control problem. We also give a second representation which can be seen as a dual problem to the first optimisation problem. We note that this is a new type of dual problem and we compare it to the standard Lagrangian dual formulation. By choosing controls in the optimisation problems we obtain upper and lower bounds on the solution to the PDE. We use these bounds to study the speed of the wave front of the PDE in the case when $\mathcal{L}$ is the generator of a suitable Lévy process.

Cette thèse est consacrée à l'étude d'équations de réaction-diffusion dans un environnement périodique en temps. Ces équations modélisent l'évolution d'une tumeur cancéreuse en présence d'un traitement qui correspond à une immunothérapie dans la première partie du manuscrit, et à une chimiothérapie cytotoxique dans la suite.On considère dans un premier temps des nonlinéarités périodiques en temps pour lesquelles 0 et 1 sont des états d'équilibre linéairement stables. On étudie l'unicité, la monotonie et la stabilité de fronts pulsatoires. On exhibe également des cas d'existence et de non-existence de telles solutions. Dans la deuxième partie de la thèse, on commence par travailler sur des nonlinéarités périodiques en temps qui sont la somme d'une fonction positive traduisant la croissance de la tumeur et d'un terme de mort de cellules cancéreuses du au traitement. On s'intéresse aux états d'équilibres de telles nonlinéarités, et on va déduire de cette étude des propriétés de propagation de perturbations et l'existence de fronts pulsatoires. On raffine ensuite le modèle en considérant des nonlinéarités qui sont la somme d'une fonction asymptotiquement périodique en temps et d'un terme perturbatif. On prouve notamment que les propriétés relatives à la propagation de perturbations restent valables dans ce cadre là. Pour finir, on s'intéresse à l'influence du protocole de traitement. / This phD thesis investigates reaction-diffusion equations in a time periodic environment. These equations model the evolution of a cancerous tumor in the presence of a treatment that corresponds to an immunotherapy in the firs part of the manuscript, and to a cytotoxic chemotherapy after. We begin by considering time-periodic nonlinearities for which 0 and 1 are linearly stable equilibrium states. We study uniqueness, monotonicity and stability of pulsating fronts. We also provide some conditions for the existence and non-existence of such solutions.In the second part of the manuscript, we begin by working on time-periodic nonlinearities which are the sum of a positive function which stands for the growth of the tumor in the absence of treatment and of a death term of cancerous cells due to treatment. We are interested in equilibrium states of such nonlinearities, and we will infer from this study spreading properties and existence of pulsating fronts. We then refine the model by considering nonlinearities which are the sum of an asymptotic periodic nonlinearity and of a small perturbation. In particular we prove that the spreading properties remain valid in this case. To finish, we are interested in the influence of the protocol of the treatment.

Langmuir turbulence in the upper ocean is generated by the interaction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves. In homogenous (neutrally stratified) shallow water, the largest scales of Langmuir turbulence are characterized by full-depth Langmuir circulation (LC). LC consists of parallel counter-rotating vortices aligned roughly in the direction of the wind. In shallow coastal shelves, LC has been observed engulfing the entire water column, interacting with the boundary layer and serving as an important mechanism for sediment re-suspension. In this research, large-eddy simulations (LES) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed deviations from classical log-layer dynamics in the surface and bottom of the water column. For example, mixing due to full-depth LC induces a large wake region eroding the classical bottom (bed) log-law velocity profile. Meanwhile, near the surface, Stokes drift shear serves to intensify small scale eddies leading to enhanced mixing and disruption of the surface velocity log-law. The modified surface and bottom log-layer dynamics induced by Langmuir turbulence and full-depth LC have important implications on Reynolds-averaged Navier-Stokes simulations (RANSS) of the general coastal ocean circulation. Turbulence models in RANSS are typically calibrated under the assumption of log-layer dynamics, which could potentially be invalid during occurrence of Langmuir turbulence and associated full-depth LC. A K-Profile Parameterization (KPP) of the Reynolds shear stress in RANSS is introduced capturing the basic mechanisms by which shallow water Langmuir turbulence and full-depth LC impact the mean flow. Single water column RANS simulations with the new parameterization are presented showing good agreement with LES

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks. KPP networks can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable. Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.