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This thesis consists of three articles all relatedin some way to eigenvalues of random matrices and theirprincipal minors and also to tilings of various planar regions with dominoes or rhombuses.Consider an $N\times N$ matrix $H_N=[h_{ij}]_{i,j=1}^N$ from the Gaussian unitary ensemble (GUE). Denote its principal minors (submatrices in the upper left corner) by $H_n=[h_{ij}]_{i,j=1}^n$ for  $n=1$, \dots, $N$. We show in paper A that  all the $N(N+1)/2$ eigenvaluesof $H_1$, \dots, $H_N$ form a determinantal process on $N$ copies of the real line $\mathbb{R}$. We also show that this distribution arises as a scaling limit in tilings of an Aztec diamond with dominoes.We discuss a corresponding result for rhombus tilings of a hexagonwhich was later proved by Okounkov and Reshtikhin. We give a new proof of that statement in the introductionto this thesis.In paper B we perform a similar analysis for the Anti-symmetric Gaussian unitary ensemble (A-GUE). We show that the positive eigenvalues of an $N\times N$ A-GUE matrix andits principal minors form a determinantal processon $N$ copies of the positive real line $\mathbb{R}^+$.We also show that this distribution of all these eigenvalues appears as a scaling limit of tilings of half a hexagon with rhombuses. In paper C we study the shuffling algorithm for tilings of an Aztec diamond. This leads to the study of an interacting set of interlacedparticles that evolve in time. We conjecture that the diffusion limit of thisprocess is a process studied by Warrenand establish some results in this direction. / QC 20100804

Web 2.0 har möjliggjort och öppnat upp för en ny typ av mellanmänsklig kommunikation. Numera kan vem som helst starta sin egen offentliga och lättillgängliga webbplattform där digitala dialoger frodas och med det skapas attraktiva marknadsplatser för företag. Enligt forskningsluckan vi har identifierat anser vi att det saknas insikter om hur företag på bästa sätt ska arbeta med bloggare utifrån bloggarnas perspektiv. Bloggar är inte bara en attraktiv marknadsplats för företag utan också för bloggarna själva som skapar sitt personliga varumärke genom att bygga upp den digitala identitet som presenteras i bloggen. Således är syftet med vår uppsats att bidra till ökad förståelse för bloggares preferenser i relationen med företag och varumärken, samt hur de väljer varumärken att beröra i sin blogg utifrån sin digitalt konstruerade identitet. För att genomföra vår studie har vi valt en kvalitativ metod med en abduktiv ansats där vi har genomfört semistrukturerade intervjuer med sju populära bloggare i Sverige. Den teoretiska referensramen som ligger till grund för vår studie är uppdelad i tre huvudkategorier; marketing public relations, word-of-mouth/word-of-blog samt personligt varumärke, där vi berör begreppen relationer, digitala dialoger, tvåvägs-symmetrisk kommunikation, digitalidentitet och källtrovärdighet. Resultatet i vår studie visar att bloggare önskar ett professionellt bemötande i relationen med PR-utövare men en personlig relation till varumärken. PR-utövare bör erbjuda bloggarna unikhet, involvering, nyhetsvärde och arvode för att skapa fördelaktiga tvåvägs-symmetriska bloggrelationer i syfte att gynna varumärket. Således förändras synen på traditionell PR vilket snarare innefattar relationer än finansiering. I vår studie presenterar vi därför en definition och modell av begreppet Blog Public Relations (BPR) vilket är vårt huvudsakliga bidrag till den vetenskapliga diskursen. Vidare visar vår undersökning att det finns tre faktorer som påverkar bloggare till att avvika från sin digitala identitet i samarbetet med företag. Förutom att de känner en press att uppdatera bloggen, och därmed ibland har valt att skriva om vissa produkter på grund av det, påverkar ett högt arvode eller ett riktigt bra och proffsigt bemötande från PR-utövarna den kommersiella avvägningen. / Web 2.0 has enabled and opened up for a new type of interpersonal communication. Nowadays, anyone can start their own public and accessible web platform where digital dialogues flourish and thus the creation of attractive markets for companies. According to the research gap we have identified, we believe that there is a lack of understanding of how companies’ best should practice blog relationships according to the bloggers. Blogs are notonly an attractive marketplace for companies but also for the bloggers themselves since they create their own personal brand by building up their digital identities that are presented in the blog. Thus, the purpose of this essay is to contribute to a better understanding of bloggers' preferences in their relationship with companies and brands and how they choose brands to mention in the blog from their digitally constructed identities. To carry out our study, we chose a qualitative method with an abductive nature where we have carried out semistructured interviews with seven popular bloggers in Sweden. The theoretical framework that forms the basis of our study is divided into three main categories; marketing public relations, word-of-mouth/word-of-blog, and personal brand, where we touch the concepts of relationships, digital dialogues, two-way symmetrical communication, digital identity and source credibility. The result of our study shows that bloggers wish for a professional approach in the relationships with PR practitioners and a personal relationship with the brands. PR practitioners should offer bloggers uniqueness, involvement, news-value and emolument to create beneficial two-way symmetric blog relationships in order to promote the brand. Moreover, this approach is changing the perception of traditional PR, which includes relationships, rather than financing. In our study, we therefore present a definition and model of the term Blog Public Relations (BPR) that is our main contribution to the scientific discourse. Furthermore, our study shows that there are three factors that influence bloggers to deviate from their digital identity in collaboration with companies. Besides that they feel pressured to update the blog, and thus sometimes chose to write about certain products because of it, a high emolument or a really good and professional behavior from PR practitioners affects the commercial balance.

After introducing concepts from convex analysis, we study how to continuously transform one convex function into another. A natural choice is the arithmetic average, as it is pointwise continuous; however, this choice fails to average functions with different domains. On the contrary, the proximal average is not only continuous (in the epi-topology) but can actually average functions with disjoint domains. In fact, the proximal average not only inherits strict convexity (like the arithmetic average) but also inherits smoothness and differentiability (unlike the arithmetic average). Then we introduce a computational framework for computer-aided convex analysis. Motivated by the proximal average, we notice that the class of piecewise linear-quadratic (PLQ) functions is closed under (positive) scalar multiplication, addition, Fenchel conjugation, and Moreau envelope. As a result, the PLQ framework gives rise to linear-time and linear-space algorithms for convex PLQ functions. We extend this framework to nonconvex PLQ functions and present an explicit convex hull algorithm. Finally, we discuss a method to find primal-dual symmetric antiderivatives from cyclically monotone operators. As these antiderivatives depend on the minimal and maximal Rockafellar functions [5, Theorem 3.5, Corollary 3.10], it turns out that the minimal and maximal function in [12, p.132,p.136] are indeed the same functions. Algorithms used to compute these antiderivatives can be formulated as shortest path problems.

People use both their hands together cooperatively in many everyday activities. The modern computer interface fails to take advantage of this basic human ability, with the exception of the keyboard. However, the keyboard is limited in that it does not afford continuous spatial input. The computer mouse is perfectly suited for the point and click tasks that are the major method of manipulation within graphical user interfaces, but standard computers have a single mouse. A single mouse does not afford spatial coordination between the two hands within the graphical user interface. Although the advent of the Universal Serial Bus has made it possible to easily plug in many peripheral devices, including a second mouse, modern operating systems work on the assumption of a single spatial input stream. Thus, if a second mouse is plugged into a Macintosh computer, a Windows computer or a UNIX computer, the two mice control the same cursor. <br /><br /> Previous work in two-handed or bimanual interaction techniques has often followed the asymmetric interaction guidelines set out by Yves Guiard's Kinematic Chain Model. In asymmetric interaction, the hands are assigned different tasks, based on hand dominance. I show that there is an interesting class of desktop user interface tasks which can be classified as symmetric. A symmetric task is one in which the two hands contribute equally to the completion of a unified task. I show that dual-mouse symmetric interaction techniques outperform traditional single-mouse techniques as well as dual-mouse asymmetric techniques for these symmetric tasks. I also show that users prefer the symmetric interaction techniques for these naturally symmetric tasks.

Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete representations of information that enables one store continuous signals as discrete, digital data with minimal error. It is this connection that allows communication engineers to realize many of our modern digital technologies including cell phones and compact disc players. This thesis focuses on certain non-Fourier generalizations of sampling theory and their applications. In particular, non-Fourier analogues of bandlimited functions and extensions of sampling theory to functions on curved manifolds are studied. New results in bandlimited function theory, sampling theory on curved manifolds, and the theory of self-adjoint extensions of symmetric operators are presented. Besides being of mathematical interest in itself, the research contained in this thesis has applications to quantum physics on curved space and could potentially lead to more efficient information storage methods in communication engineering.

People use both their hands together cooperatively in many everyday activities. The modern computer interface fails to take advantage of this basic human ability, with the exception of the keyboard. However, the keyboard is limited in that it does not afford continuous spatial input. The computer mouse is perfectly suited for the point and click tasks that are the major method of manipulation within graphical user interfaces, but standard computers have a single mouse. A single mouse does not afford spatial coordination between the two hands within the graphical user interface. Although the advent of the Universal Serial Bus has made it possible to easily plug in many peripheral devices, including a second mouse, modern operating systems work on the assumption of a single spatial input stream. Thus, if a second mouse is plugged into a Macintosh computer, a Windows computer or a UNIX computer, the two mice control the same cursor. <br /><br /> Previous work in two-handed or bimanual interaction techniques has often followed the asymmetric interaction guidelines set out by Yves Guiard's Kinematic Chain Model. In asymmetric interaction, the hands are assigned different tasks, based on hand dominance. I show that there is an interesting class of desktop user interface tasks which can be classified as symmetric. A symmetric task is one in which the two hands contribute equally to the completion of a unified task. I show that dual-mouse symmetric interaction techniques outperform traditional single-mouse techniques as well as dual-mouse asymmetric techniques for these symmetric tasks. I also show that users prefer the symmetric interaction techniques for these naturally symmetric tasks.

Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete representations of information that enables one store continuous signals as discrete, digital data with minimal error. It is this connection that allows communication engineers to realize many of our modern digital technologies including cell phones and compact disc players. This thesis focuses on certain non-Fourier generalizations of sampling theory and their applications. In particular, non-Fourier analogues of bandlimited functions and extensions of sampling theory to functions on curved manifolds are studied. New results in bandlimited function theory, sampling theory on curved manifolds, and the theory of self-adjoint extensions of symmetric operators are presented. Besides being of mathematical interest in itself, the research contained in this thesis has applications to quantum physics on curved space and could potentially lead to more efficient information storage methods in communication engineering.

A formulation is proposed for the boundary element analysis of poro-elastic media with axi-symmetric geometry. The boundary integral equation is reduced to a set of line integral equations in the generating plane for each of the Fourier coefficients, through complex Fourier series expansion of boundary quantities in circumferential direction. The method is implemented into a computer program, where the fundamental solutions are integrated by Gaussian Quadrature along the generator, while Fast Fourier Transform algorithm is employed for integrations in circumferential direction. The strongly singular integrands in boundary element equations are regularized by a special technique. The Fourier transform solution is then inverted in to R&amp / #952 / z space via inverse FFT. The success of the method is assessed by problems with analytical solutions. A good fit is observed in each case, which indicates effectiveness and reliability of the present method.

A mixture experiment is an experiment in which the k ingredients are nonnegative and subject to the simplex restriction £Ux_i=1 on the (k-1)-dimensional probability simplex S^{k-1}. This dissertation discusses optimal designs for linear and quadratic log contrast models for experiments with mixtures suggested by Aitchison and Bacon-Shone (1984), where the experimental domain is restricted further as in Chan (1992). In this study, firstly, an essentially complete class of designs under the Kiefer ordering for linear log contrast models with mixture experiments is presented. Based on the completeness result, £X_p-optimal designs for all p, -¡Û<p≤1 including D- and A-optimal are obtained, where the eigenvalues of the design moment matrix are used. By using the approach presented here, we gain insight on how these £X_p-optimal designs behave. Following that, the exact N-point D-optimal designs for linear log contrast models with three and four ingredients are further investigated. The results show that for k=3 and N=3p+q ,1 ≤q≤2, there is an exact N-point D-optimal design supported at the points of S_1 (S_2) with equal weight n/N, 0≤n≤p , and puts the remaining weight (N-3n)/N uniformly on the points of S_2 (S_1) as evenly as possible, where S_1 and S_2 are sets of the supports of the approximate D-optimal designs. When k=4 and N=6p+q , 1 ≤q≤5, an exact N-point design which distributes the weights as evenly as possible among the supports of the approximate D-optimal design is proved to be exact D-optimal. Thirdly, the approximate D_s-optimal designs for discriminating between linear and quadratic log contrast models for experiments with mixtures are derived. It is shown that for a symmetric subspace of the finite dimensional simplex, there is a D_s-optimal design with the nice structure that puts a weight 1/(2^{k-1}) on the centroid of this subspace and the remaining weight is uniformly distributed on the vertices of the experimental domain. Moreover, the D_s-efficiency of the D-optimal design for quadratic model and the design given by Aitchison and Bacon-Shone (1984) are also discussed Finally, we show that an essentially complete class of designs under the Kiefer ordering for the quadratic log contrast model is the set of all designs in the boundary of T or origin of T . Based on the completeness result, numerical £X_p -optimal designs for some p, -¡Û<p≤1 are obtained.