This paper considers the problem of model uncertainty associated with variable selection and specification of the spatial weight matrix in spatial growth regression models in general and growth regression models based on the matrix exponential spatial specification in particular. A natural solution, supported by formal probabilistic reasoning, is the use of Bayesian model averaging which assigns probabilities on the model space and deals with model uncertainty by mixing over models, using the posterior model probabilities as weights. This paper proposes to adopt Bayesian information criterion model weights since they have computational advantages over fully Bayesian model weights. The approach is illustrated for both identifying model covariates and unveiling spatial structures present in pan-European growth data. (authors' abstract) / Series: Department of Economics Working Paper Series

Made available in DSpace on 2015-05-15T11:46:12Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1062540 bytes, checksum: 59af76713b0f39a5f68815eb132bc18e (MD5) Previous issue date: 2013-03-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, we study existence, multiplicity and nonexistence of positive solutions, with respect to a positive parameter , for a class of quasilinear elliptic problems in bounded domains of RN, N 2, involving the N-laplacian operator and a nonlinearity f(t) which behaves as t, for some 2 (0;N1), when t ! 0+ and has critical exponential growth of Trudinger-Moser type at +1. In order to obtain the results, we have used minimax theorems, sub and supersolution methods and a refinement of the Trudinger- Moser inequality due to P.-L. Lions. / Neste trabalho, estudamos existência, multiplicidade e não-existência de soluções positivas, com respeito a um parâmetro positivo , para uma classe de problemas elípticos quasilineares em domínios limitados de RN, N 2, envolvendo o operador N-laplaciano e uma não-linearidade f(t) que se comporta como tá, para algum 2 (0;N 1), quando t ! 0+ e possui crescimento crítico exponencial do tipo Trudinger-Moser em +1. Na obtenção dos resultados, podemos destacar a utilização de teoremas do tipo minimax, métodos de sub e supersolução e um refinamento da Desigualdade de Trudinger-Moser devido a P.-L. Lions.

In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hamiltonian systems in bounded domains with potential function identically zero. The second case deals with systems of equations on the whole space, the potential function is bounded from below for some positive constant and satisfies some integrability conditions, while the nonlinearities involve weight functions containing a singulatity at the origin. In the third case, we consider systems with coercivity potential functions and nonlinearities with weight functions which may have singularity at the origin or decay at infinity. In the last case, we study Hamiltonian systems, where the potential can be unbounded or can vanish at infinity. To establish the existence of solutions, we use variational methods combined with Trudinger-Moser type inequalities for Lorentz-Sobolev spaces and a finite-dimensional approximation. / Neste trabalho estudamos a existência de soluções fracas não triviais para sistemas hamiltonianos do tipo elíptico, em dimensão dois, envolvendo uma função potencial e não linearidades tendo crescimento exponencial máximo com respeito a uma curva (hipérbole) crítica. Consideramos quatro casos diferentes. Primeiramente estudamos sistemas de equações em domínios limitados com potencial nulo. No segundo caso, consideramos sistemas de equações em domínio ilimitado, sendo a função potencial limitada inferiormente por alguma constante positiva e satisfazendo algumas de integrabilidade, enquanto as não linearidades contêm funções-peso tendo uma singularidade na origem. A classe seguinte envolve potenciais coercivos e não linearidades com funções peso que podem ter singularidade na origem ou decaimento no infinito. O quarto caso é dedicado ao estudo de sistemas em que o potencial pode ser ilimitado ou decair a zero no infinito. Para estabelecer a existência de soluções, utilizamos métodos variacionais combinados com desigualdades do tipo Trudinger-Moser em espaços de Lorentz-Sobolev e a técnica de aproximação em dimensão finita.

People use shortcuts to make decisions to efficiently deal with a large volume of information. Linear thinking is one shortcut and it contributes to exponential growth bias which means underestimation of exponential growth values. This study examined differences in exponential growth bias in the context of the stock market and COVID-19 cases. Moreover, this research analyzed correlation between exponential growth bias and worry for health and for the economy in the contexts of COVID-19 and stock market. A total of 120 participants completed an online survey in which they were randomly assigned to the COVID-19 or stock market group. A 2 x 3 repeated measures ANOVA showed no significant differences depending on the group. Moreover, ANOVA showed that bias increased in line with the increase in the percentages analyzed for both groups. Exploratory Pearson analysis showed that there was a significant negative correlation between worry for the economy and exponential growth bias of 15% and 40% growth scenarios in COVID-19 group. There were no significant correlations between worry for the economy or health in the stock market group. The conclusion is that people use shortcuts which leads them to biased decision- making. For example, when calculating exponential values, people think linearly and it leads them to exponential growth bias, what in practice results in estimating values lower than they are. Interventions, as education with aim to reduce exponential growth bias are proposed for the future research.

In introductory biology, college students are taught to predict how populations will grow and change over time by using population growth models. These models are commonly represented as mathematical equations. However, students consistently struggle when math and biology concepts intersect in the classroom, and these struggles lead to suboptimal understanding of how mathematical population models are designed and used. Education literature suggests that students may struggle with population modeling because of math anxiety, the high cognitive load of the task, and the lack of scaffolding for abstract concepts. In our study, we sought to improve student mastery modeling exponential growth, logistic growth, and Lotka-Volterra predator-prey interactions through using pictorial diagrams in modeling pedagogy. We predicted that these diagrams would reduce the amount of triggered math anxiety, lower the cognitive load of the task through reducing element interactivity, and allow for a more scaffolding for abstract symbols through a pictorial representation bridge. To test the effectiveness of population diagrams, we created two versions of a population modeling lesson plan: one version taught using diagrams then equations, while the other taught using purely equations. We also designed practice and assessment questions that tested calculation and model-building ability. We assessed math anxiety, scientific reasoning ability, and math ability at the beginning of the semester and state anxiety, effort of tasks, and difficulty of tasks during each lesson. Over 200 students from a non-major biology course were randomly assigned to each group, and all were given a pre-assessment, four lessons, a practice test, and a unit test on population modeling. Our findings show that while the addition of pictorial models to the traditional pedagogy did not have a significant effect on exponential and logistic growth model mastery, students that were exposed to predator-prey diagrams were more able to create a new model for a three-level predator-prey interaction than students that were only given traditional pedagogy. In addition, students who were exposed to predator-prey interaction diagrams before they derived equations reported a lower cognitive load than students who were only exposed to equations. Although diagrams were not a more helpful calculation tool for students than traditional equations, using population diagrams before to equation derivation may help improve student mastery of growth model creation.

<p>Disturbances introduced in wall-bounded .ows can grow andlead to transition from laminar to turbulent .ow. In order toreduce losses or enhance mixing in energy systems, afundamental understanding of the .ow stability is important. Inlow disturbance environments, the typical path to transition isan exponential growth of modal waves. On the other hand, inlarge disturbance environments, such as in the presence of highlevels of free-stream turbulence or surface roughness,algebraic growth of non-modal streaks can lead to transition.In the present work, the stability of wall-bounded .ows isinvestigated by means of linear stability equations valid bothfor the exponential and algebraic growth scenario. Anadjoint-based optimization technique is used to optimize thealgebraic growth of streaks. The exponential growth of waves ismaximized in the sense that the envelope of the most ampli.edeigenmode is calculated. Two wall-bounded .ows areinvestigated, the Falkner–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan boundary layer, theoptimization is carried out over the initial streamwiselocation as well as the spanwise wave number and the angularfrequency. Furthermore, a uni.ed transition-prediction methodbased on available experimental data is suggested. The Blasiuswall jet is matched to the measured .ow in an experimentalwall-jet facility. Linear stability analysis with respect tothe growth of two-dimensional waves and streamwise streaks areperformed and compared to the experiments. The nonlinearinteraction of introduced waves and streaks and the .owstructures preceding the .ow breakdown are investigated bymeans of direct numerical simulations.</p><p>Descriptors: Boundary layer, wall jet, algebraic growth,exponential growth, lift-up e.ect, streamwise streaks,Tollmien-Schlichting waves, free-stream turbulence, roughnesselement, transition prediction, Parabolized StabilityEquations, Direct Numerical Simulation.</p>

Polymer/inorganic nanoparticle hybrid thin films, primarily composed of functional inorganic nanoparticles, are of great interest to researchers because of their interesting electronic, photonic, and optical properties. In the past two decades, layer-by-layer (LbL) assembly has become one of the most powerful techniques to fabricate such hybrid thin films. This method offers an easy, inexpensive, versatile, and robust fabrication technique for multilayer formation, with precisely controllable nanostructure and tunable properties. In this thesis, various ways to control the structure of hybrid thin films, primarily composed of polyelectrolytes and indium tin oxide (ITO), are the main topics of study. ITO is one of the most widely used conductive transparent oxides (TCOs) for applications such as flat panel displays, photovoltaic cells, and functional windows. In this work, polyethyleneimine (PEI) was used to stabilize the ITO suspensions and improve the film buildup rate during the LbL assembly of poly(sodium 4-styrenesulfonate) (PSS) and ITO. The growth rate was doubled due to the stronger interaction forces between the PSS and PEI-modified ITO layer. The assembly of hybrid films was often initiated by a polyelectrolyte precursor layer, and the characteristics of the precursor layer were found to significantly affect the assembly of the hybrid thin films. The LbL assembly of ITO nanoparticles was realized on several substrates, including cellulose fibers, write-on transparencies, silicon wafers, quartz crystals, and glasses. By coating the cellulose fibers with ITO nanoparticles, a new type of conductive paper was manufactured. By LbL assembly of ITO on write-on transparencies, transparent conductive thin films with conductivity of 10⁻⁴ S/cm and transparency of over 80 % in the visible range were also prepared. As a result of this work on the mechanisms and applications of LbL grown films, the understanding of the LbL assembly of polyelectrolytes and inorganic nanoparticles was significantly extended. In addition to working with ITO nanoparticles, this thesis also demonstrated the ability to grow bicomponent [PEI/SiO₂]n thin films. It was further demonstrated that under the right pH conditions, these films can be grown exponentially (e-LbL), resulting in much thicker films, consisting of mostly the inorganic nanoparticles, in much fewer assembly steps than traditional linearly grown films (l-LbL). These results open the door to new research opportunities for achieving structured nanoparticle thin films, whose functionality depends primarily on the properties of the nanoparticles.

It is widely known that surfaces play an important role in numerous biological processes and technological applications. Thus, being able to modify surface properties provides an opportunity to control many phenomena occurring at interfaces. One way of controlling surface properties is to adsorb a polymer film onto the surface, for example through layer-by-layer (LbL) deposition of polyelectrolytes. This simple but versatile technique enables various polymers, proteins, colloidal particles etc. to be incorporated into the film, resulting in a multifunctional coating. Due to recent legislations and a consumer demand for more environmentally friendly products, we have chosen to use natural polymers (biopolymers) from renewable resources. The focus of this thesis has been on the adsorption of biopolymers and their layer-by-layer formation at solid-liquid interfaces; these processes have been studied by a wide range of techniques. The main method was the quartz crystal microbalance with dissipation monitoring (QCM-D), which measures the adsorbed mass, including trapped solvent and the viscoelastic properties of an adsorbed film. This technique was often complemented with an optical method, such as ellipsometry or dual polarization interferometry (DPI), which provided information about the “dry” polymer or protein adsorbed mass. From this combination, the solvent content and density of the layers was evaluated. In addition, the surface force apparatus (SFA), X-ray photoelectron spectroscopy (XPS), total internal reflection fluorescence (TIRF), and fluorescence resonance energy transfer (FRET) were utilized, providing further information about the film structure, chemical composition, and polymer inter-layer diffusion. Adsorption studies of the glycoprotein mucin, which has a key role in the mucousal function, showed that despite the net negative charge of mucin, it adsorbed on negatively charged substrates. The adsorbed layer was highly hydrated and the segment density on the substrate was low. We showed the importance of characterizing the mucin used, since differences in purity, such as the presence of albumin, gave rise to different adsorption behaviours in terms of both adsorbed amount and structure. The adsorbed mucin layer was to a large extent desorbed upon exposure to the anionic surfactant sodium dodecyl sulfate (SDS). In order to prevent desorption, we demonstrated that a protective layer of the cationic polysaccharide chitosan could be adsorbed onto the mucin layer and that the mucin-chitosan complexes resisted the desorption normally induced by association with SDS. Moreover, the association between chitosan and SDS was examined at the solid-liquid interface, in the bulk, and at the air-water interface. In all these environments chitosan-SDS complexes were formed and a net charge reversal of the complexes from positive to negative was observed when the concentration of SDS was increased. Furthermore, the LbL deposition method could be used to form a multilayer-like film by alternate adsorption of mucin and chitosan on silica substrates. The LbL technique was also applied to two proteins, lysozyme and β-casein with the aim of building a multilayer film consisting entirely of proteins. These proteins formed complexes at the solid-liquid interface, resulting in a proteinaceous layer, but the build-up was highly irregular with an increase in adsorbed amount per protein deposition cycle that was far less than a monolayer.Continuing with chitosan, known to have antibacterial properties we assembled multilayers with an anti-adhesive biopolymer, heparin, to evaluate the potential of this system as a coating for medical implants. Multilayers were assembled under various solution deposition conditions and the film structure and dynamics were studied in detail. The chitosan-heparin film was highly hydrated, in the range 60-80 wt-% depending on the deposition conditions. The adsorbed amount and thickness of the film increased exponential-like with the number of deposition steps, which was explained by inter-diffusion of chitosan molecules in the film during the build-up. In a novel approach, we used the distant dependent FRET technique to prove the inter-layer diffusion of fluorescent-labelled chitosan molecules within the film. The diffusion coefficient was insignificantly dependent on the deposition pH and ionic strength, and hence on the film structure. With the use of a pH sensitive dye buried under seven chitosan-heparin bilayers, we showed that the dye remained highly sensitive to the charge of the outermost layer. From complementary QCM-D data, we suggested that an increase in the energy dissipation does not necessarily indicate that the layer structure becomes less rigid. / Det är välkänt att ytor spelar en viktig roll i många biologiska processer och tekniska tillämpningar. Att kunna modifiera en ytas egenskaper ger därför en möjlighet att kunna kontrollera många fenomen som sker på ytor. Ett sätt att kontrollera ytegenskaperna är genom att adsorbera en polymerfilm på ytan, till exempel genom att växelvis adsorbera olika polyelektrolyter (LbL-teknik). Denna enkla men mångsidiga teknik möjliggör att många olika material kan införlivas i filmen, vilket resulterar i en multifunktionell beläggning. På grund av dagens lagstiftning och konsumenters ökade efterfrågan på miljövänliga material beslutade vi oss för att använda biologiska polymerer (biopolymerer) i detta projekt. Fokus i den här avhandlingen har varit på adsorption av biopolymerer och deras LbL-formation på gränsytan vätska-fast fas, där adsorptionsförloppet och det adsorberade skiktet bestående av biopolymerer studerats med en mängd olika tekniker. Huvudtekniken var kvartskristallmikrovåg med energidissipations-registrering (QCM-D), som mäter massan inklusive inkorporerat vatten, samt de viskoelastiska egenskaperna hos ett adsorberat skikt. Som komplement till denna teknik användes ofta optiska metoder, till exempel ellipsometri och ”dubbel polarisationsinterferometri (DPI)”, två tekniker som endast mäter massan av de adsorberade biopolymererna. Genom denna kombination av metoder kunde massan av inkorporerat vatten i filmen och filmens densitet bestämmas. Dessutom användes ytkraftsapparaten (SFA), röntgenfotoelektronspektrometri (XPS), och fluorescens-spektroskopiteknikerna TIRF och FRET i några undersökningar för att erhålla information om skiktens struktur, kemiska sammansättning och polymerernas diffusion inom skiktet.Adsorptionsstudier av glycoproteinet mucin, som har en central roll i funktionen av slemhinnan, avslöjade att trots att mucinet har en negativ nettoladdning adsorberade det ändå på negativt laddade substrat. Det adsorberade lagret var väldigt hydratiserat och hade en låg andel mucin i direkt kontakt med ytan. Vi påvisade vikten av att noga undersöka mucinet som användes, eftersom olika renhet, till exempel i form av förekomsten av albumin gav upphov till olika adsorptionsbeteende gällande både adsorberad mängd och struktur. En stor andel av det adsorberade mucinlagret desorberade när det exponerades för den anjoniska tensiden natriumdodecylsulfat, SDS. Vi visade att ett skyddande lager av den katjoniska polysackariden chitosan kunde adsorberas på mucinet och att mucin-chitosan-komplexen inte desorberade när SDS tillsattes. Därtill studerades växelverkan mellan chitosan och SDS på gränsytan vätska-fast fas, i bulken och på luft-vattengränsytan. Komplex av chitosan-SDS bildades i samtliga miljöer och en nettoladdningsomsvängning från positiv till negativ observerades när koncentrationen av SDS ökades.Vidare kunde LbL-tekniken nyttjas för att skapa ett multilagerlikt skikt genom att alternerande adsorbera mucin och chitosan på kiseldioxidsubstrat. Denna teknik användes även med två proteiner, lysozym och β-kasein, med målet att skapa ett multilager bestående av endast proteiner. Dessa proteiner bildade komplex på gränsytan vätska-fast fas i form av ett blandat proteinlager, men uppbyggnaden var väldigt oregelbunden med en ökning i adsorberad mängd per proteindeponeringscykel som var avsevärt mindre än ett monolager.Inom området för biomaterial utgör de antibakteriella och antihäftande egenskaperna hos chitosan respektive heparin en lovande blandning för beläggningar av medicinska implantat. Baserat på detta konstruerade vi multilagerfilmer av chitosan och heparin med olika deponeringslösningar och undersökte dynamiken och filmens struktur i detalj. Chitosan-heparin-filmen var starkt hydratiserad, bestående av cirka 60-80 vikt-% vatten beroende på deponeringsbetingelserna. Den adsorberade mängden och tjockleken på filmen ökade nästan exponentiellt med antal deponeringar, vilket förklarades med chitosanets förmåga att diffundera genom filmen under uppbyggnaden. Med ett nytt angreppssätt använde vi FRET för att bevisa diffusionen av fluorescerande färgmärkt chitosan i filmen under uppbyggnaden. Diffusionskoefficienten var i princip oberoende av pH och jonstyrka under deponeringen och följaktligen av filmens struktur. Genom att använda ett pH-känsligt färgämne begravt under sju biskikt av chitosan-heparin visade vi att färgämnet i hög grad påverkades av laddningen på det yttersta lagret. Från QCM-D-data lade vi fram teorin om att en ökning av energidissipationen för ett lager inte nödvändigtvis indikerar att lagrets struktur har blivit mindre styvt. / QC 20100729

Made available in DSpace on 2015-05-15T11:46:22Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1317724 bytes, checksum: 6a915301a18806d377bf5c949922b304 (MD5) Previous issue date: 2013-05-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, we will study the existence and multiplicity of weak solutions for a class of nonhomogeneous elliptic problems involving exponential growth Trudinger-Moser type in R2. For this, we will use the Ekeland s Variational Principle and the Mountain Pass Theorem without the Palais-Smale condition in combination with a version of the Trudinger-Moser inequality. / Teorema do Passo da Montanha, Principio variacional de Ekeland, equação de Schrodinger, Desigualdade de Trudinger-Moser, Crescimento Exponencial.

Disturbances introduced in wall-bounded .ows can grow andlead to transition from laminar to turbulent .ow. In order toreduce losses or enhance mixing in energy systems, afundamental understanding of the .ow stability is important. Inlow disturbance environments, the typical path to transition isan exponential growth of modal waves. On the other hand, inlarge disturbance environments, such as in the presence of highlevels of free-stream turbulence or surface roughness,algebraic growth of non-modal streaks can lead to transition.In the present work, the stability of wall-bounded .ows isinvestigated by means of linear stability equations valid bothfor the exponential and algebraic growth scenario. Anadjoint-based optimization technique is used to optimize thealgebraic growth of streaks. The exponential growth of waves ismaximized in the sense that the envelope of the most ampli.edeigenmode is calculated. Two wall-bounded .ows areinvestigated, the Falkner–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan boundary layer, theoptimization is carried out over the initial streamwiselocation as well as the spanwise wave number and the angularfrequency. Furthermore, a uni.ed transition-prediction methodbased on available experimental data is suggested. The Blasiuswall jet is matched to the measured .ow in an experimentalwall-jet facility. Linear stability analysis with respect tothe growth of two-dimensional waves and streamwise streaks areperformed and compared to the experiments. The nonlinearinteraction of introduced waves and streaks and the .owstructures preceding the .ow breakdown are investigated bymeans of direct numerical simulations. Descriptors: Boundary layer, wall jet, algebraic growth,exponential growth, lift-up e.ect, streamwise streaks,Tollmien-Schlichting waves, free-stream turbulence, roughnesselement, transition prediction, Parabolized StabilityEquations, Direct Numerical Simulation. / NR 20140805