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We study the problem of detecting top-k events from digital interaction records (e.g, emails, tweets). We first introduce interaction meta-graph, which connects associated interactions. Then, we define an event to be a subset of interactions that (i) are topically and temporally close and (ii) correspond to a tree capturing information flow. Finding the best event leads to one variant of prize-collecting Steiner-tree problem, for which three methods are proposed. Finding the top-k events maps to maximum k-coverage problem. Evaluation on real datasets shows our methods detect meaningful events.

This thesis starts from the Matsuda and Abrams paper 'Timid Consumers: Self-Extinction Due to Adaptive Change in Foraging and Anti-predator Effort.' Matsuda and Abrams show an example of evolutionary suicide due to the evolution of prey timidity in a predator-prey model with a Holling type II functional response. The key assumption they use to obtain evolutionary suicide is that the predator population size is kept constant. In this thesis, we relax this assumption by introducing a second type of prey to the model and investigate whether evolutionary suicide may still occur according to the evolution of timidity in the first prey species. To study this in the long-term, we use the theory of adaptive dynamics. Firstly, we analyse the limit case where the predator dynamics depend only upon the second prey species. Predators still hunt the evolving prey either as a snack or for entertainment without gaining any energy. Under this hypothesis, our model reproduces Matsuda and Abrams' results both qualitatively and quantitatively. Moreover, the introduction of the second type of prey allows for the appearance of limit cycles as dynamical attractors. We detect a fold bifurcation in the stability of the limit cycles when the first type of prey timidity increases. Thus, we are able to construct an example of evolutionary suicide on a fold bifurcation of limit cycles. Furthermore, we perform critical function analysis on the birth rate of the evolving prey as a function of prey timidity. We derive general conditions for the birth rate function that assure the occurrence of evolutionary suicide. Secondly, we analyse the full model without making any simplifying assumptions. Because of the analytical complexity of the system we use numerical bifurcation analysis to study bifurcations of the internal equilibria. More specifically, we utilize the package MatCont to carry out equilibria continuation. In this way, we are able to estimate the range of parameters where the results of Matsuda and Abrams' model hold. Starting from the parameter set that reproduce Matsuda and Abrams' results quantitatively we track the fold bifurcation and show that evolutionary suicide occurs for a considerably wide range of parameters. Moreover, we find that in the full model evolutionary suicide may also occur through a subcritical Hopf bifurcation.

In this thesis we formulate and analyze a structured population model, with infectious disease dynamics, based on a similar life-cycle as with individuals of the Hamilton-May model. Each individual is characterized by a strategy vector (state dependent dispersal), and depending on the infectious status of the individual, it will use a strategy accordingly. We begin by assuming that every individual in the population has the same strategy, and as the population equilibriates we consider a mutant, with it's own strategy, entering the population, trying to invade. We apply the theory of Adaptive dynamics to model the invasion fitness of the mutant, and to analyze the evolution of dispersal. We show that evolutionary branching is possible, and when such an event happens, the evolutionary trajectories, described by the Canonical equation of Adaptive dynamics, of two strategies evolve into the extinction of one branch. The surviving branch then evolves to the extinction of the disease.

Recent biomathematical literature has suggested that, under the assumption of a trade-off between replication speed and fidelity, a pathogen can evolve to more than one optimal mutation rate. O'Fallon (2011) presents a particularly compelling case grounded in simulation. In this thesis, we treat the subject analytically, approaching it through the lens of adaptive dynamics. We formulate a within-host model of the pathogen load starting from assumptions at the genomic level, explicitly accounting for the fact that most mutations are deleterious and stunt growth. We single out the pathogen's mutation probability as the evolving trait that distinguishes strains from one another. Our between-host dynamics take the form of an SI model, first without superinfection and later with two types of non-smooth superinfection function. The pathogen's virulence and transmission rate are functions of the within-host equilibrium pathogen densities. In the case of our mechanistically defined superinfection function, we uncover evolutionary branching in conjunction with two transmission functions, one a caricatural (expansion) example, the other a more biologically realistic (logistic) one. Because of the non-smoothness of the mechanistic superinfection function, our branching points are actually one-sided ESSs à la Boldin and Diekmann (2014). When branching occurs, two strains with different mutation probabilities both ultimately persist on the evolutionary timescale.

Artificial agents are commonly used in games to simulate human opponents. This allows players to enjoy games without requiring them to play online or with other players locally. Basic approaches tend to suffer from being unable to adapt strategies and often perform tasks in ways very few human players could ever achieve. This detracts from the immersion or realism of the gameplay. In order to achieve more human-like play more advanced approaches are employed in order to either adapt to the player's ability level or to cause the agent to play more like a human player can or would. Utilizing artificial neural networks evolved using the NEAT methodology, we attempt to produce agents to play a FPS-style game. The goal is to see if the approach produces well-playing agents with potentially human-like behaviors. We provide a large number of sensors and motors to the neural networks of a small population learning through co-evolution. Ultimately we find that the approach has limitations and is generally too slow for practical application, but holds promise for future developments. Many extensions are presented which could improve the results and reduce training times. The agents learned to perform some basic tasks at a very rough level of skill, but were not competitive at even a beginner level.

Mobiililiittymien käyttö on muuttunut viimeisen puolen vuosikymmenen aikana huomattavasti mobiilidatan käytön kasvaessa merkittävästi ja ala on edelleen jatkuvassa murroksessa. Tällaisessa muuttuvan markkinan tilanteessa on tärkeää niin markkinaviranomaisille kuin alan yrityksillekin ymmärtää kuluttajien mielipiteitä ja toimintaa. Tässä tutkielmassa selvitetään kuluttajatyytymättömyyteen sekä operaattorin vaihtoon vaikuttavia tekijöitä mobiiliviestintäalalla Pohjoismaissa. Tekijöiden selvittämiseen käytetään logistista regressiomallia suurimman uskottavuuden estimoinnilla ja tulokset varmennetaan Exact logistisella regressiomallilla aineiston vinoumasta johtuen. Tutkielman aineistona käytetään Euroopan Komission keräämää eri toimialoihin liittyvää kyselyaineistoa. Taustateorian osalta tutkielmassa syvennytään kuluttajatyytymättömyyden käsitteeseen sekä tyytymättömän kuluttajan toimintamahdollisuuksiin. Kuluttajatyytymättömyyttä havaittiin kasvattavan mobiililiittymän kanssa koetut ongelmatilanteet sekä vastaajan matala luottamus alan toimijoihin ja vähentävän vastaajan suomalaisuus sekä erittäin hyvä taloudellinen tilanne. Operaattorin vaihdon todennäköisyyttä havaittiin kasvattavan mobiililiittymän kanssa koettujen ongelmatilanteiden aiheuttama aineellinen tai henkinen suuri haitta sekä Tanska vastaajan kotimaana. Vaihdon todennäköisyyttä laski Ruotsi vastaajan kotimaana ja internetin harva käyttö. Tulokset olivat yhdensuuntaisia molemmilla estimointimenetelmillä kummassakin mallinnuskohteessa.

This thesis is about the existence and uniqueness of a solution for the semilinear heat equation of polynomial type. The extensive study of properties for these equations started off in the 1960s, when Hiroshi Fujita published his results that the existence and uniqueness of solutions depends critically on the exponent of the nonlinear term. In this thesis we expose some of the basic methods used in the theory of linear, constant coefficient partial differential equations. These considerations lay out the groundwork for the main result of the thesis, which is the existence and uniqueness of a solution to the generalized heat equation. In Chapter 2 we expose the basics of functional analysis. We start off by defining Banach spaces and provide some examples of them. Then, we state the very useful Banach fixed point theorem, which guarantees the existence and uniqueness of a solution to certain types of integral equations. Next, we consider linear maps between normed spaces, with a focus on linear isomorphisms, which are linear maps preserving completeness. The isomorphisms prove to be very useful, when we consider weighted spaces. This is because for certain types of weights, we can identify the multiplication by weight with a linear isomorphism. In Chapter 3 we introduce the Fourier transform, which is a highly useful tool for studying linear partial differential equations. We go through its basic mapping properties, such as, interaction with derivatives and convolution. Then, we consider useful spaces in Fourier analysis. Chapter 4 is on the regular, inhomogeneous heat equation. A common method for deriving the solution to heat equation is formally applying the Fourier transform to it. This way we obtain a first order, linear ordinary differential equation, for which there is a known solution. The derived solution will serve as a motivator for how to approach the semilinear case. Also, in the end we will solve explicitly a slight generalization of the heat equation. In Chapter 5 we prove the main result of this thesis: existence and uniqueness of a generalized solution for the semilinear heat equation. The methods we use in the proof are quite elementary in the sense that we do not need heavy mathematical machinery. We reformulate the generalized semilinear heat equation using an operator and show that it satisfies the conditions of the Banach fixed point theorem in a small, closed ball of a suitable Banach space. We also include an appendix, in which we discuss differentiability properties of the generalized solution. It is possible to apply methods used in the proof of the generalized case to prove continuous differentiability. We provide some ideas on how one should approach the time differentiability of the solution by estimating the difference quotient of the integral operator.

The Smoluchowski coagulation equation is considered to be one of the most fundamental equations of the classical description of matter alongside with the Boltzman, Navier-Stokes and Euler equations. It has applications from physical chemistry to astronomy. In this thesis, a new existence result of measure valued solutions to the coagulation equation is proven. The proven existence result is stronger and more general than a previously claimed result. The proven result holds for a generic class of coagulation kernels, including various kernels used in applications. The coagulation equation models binary coagulation of objects characterized by a strictly positive real number called size, which often represents mass or volume in applications. In binary coagulation, two objects can merge together with a rate characterized by the so-called coagulation kernel. Time evolution of the size distribution is given by the coagulation equation. Traditionally the coagulation equation has two forms, discrete and continuous, which are referring to whether the objects sizes can take discrete or continuous values. A similar existence result to the one proven in this thesis has been obtained for the continuous coagulation equation, while the discrete coagulation equation is often favored in applications. Being able to study both discrete and continuous systems and their mixtures at the same time has motivated the study of measure valued solutions to the coagulation equation. After motivating the existence result proven in this thesis, its proof is organized into four Steps described at the end of the introduction. The needed mathematical tools and their connection to the four Steps are presented in chapter 2. The precise mathematical statement of the existence result is given in chapter 3 together with Step 1, where the coagulation equation will be regularized using a parameter ε ∈ (0, 1) into a more manageable regularized coagulation equation. Step 2 is done in chapter 4 and it consists of proving existence and uniqueness of a solution f_ε for each regularized coagulation equation. Step 3 and Step 4 are done in chapter 5. In Step 3, it will be proven that the regularized solutions {f_ε} have a converging subsequence in the topology of uniform convergence on compact sets. Step 4 finishes the existence proof by verifying that the subsequence’s limit satisfies the original coagulation equation. Possible improvements and future work are outlined in chapter 6.

The conventional understanding and model of development is based on economic growth. This dominant way of creating development has consequences to natural, cultural and social environments, which cannot be overlooked. The transformations within these environments are increasingly connected to the prevailing socio-economic model of neoliberalism, but are often not considered in its contextualization at a local scale. The processes of production of space and nature under the neoliberal doctrine have led to economic restructuration and to conformation of geographies of neoliberal environment, which together transform localities. There is an increasing need to investigate how the local inhabitants understand and experience these processes and their outcomes. In this research, place is introduced as an insight to observe these problematics. Place in this research is understood as a changing and dynamic terrain, which articulates experiences of development. This research is qualitative case study which investigates the consequences of production of space and nature in Curepto, Chile. Curepto is one of the localities where the implementation of a normative framework for economic growth has resulted in extensive areas of foreign tree species monoculture and important physical and socio-spatial transformations related to them. The primary aim of this research is to investigate the local inhabitants' accounts of these transformations. The thesis investigates how the locality has changed, but focuses on what these changes have meant for the local community and their sense of place. Physical, sociocultural and emotive dimensions of place as well as their transformations were investigated using qualitative methods, mainly semi-structured interviews. Residents were interviewed both in urban and rural districts. The findings of this research indicate that the forest industry and tree plantations have been important drivers behind the physical and socio-spatial transformations. The extensive plantations of pine and eucalyptus have changed the physical environment and these transformations are reflected in the social and cultural geography. Environmental degradation, changed circumstances of land property, loss of native forests and drought constitute transformations that affect livelihoods negatively especially in the rural districts, and come in parallel with a loss of local tradition and culture. The meaningful space the inhabitants experience diminishes and is made more one-sided, as access to the natural environment becomes more difficult and the interaction with it is lost. Although transformations within place are considered negative, the meaningful relation inhabitants have with place remains positive. Participants redetermine their practices and livelihoods, and re-articulate the relation with their surroundings in order to stay in their place. The local community lives in a space that is both familiar and foreign to them, loved and hated at the same time.

Perovskites are a class of materials that possess many interesting properties with a wide range of technological applications in the field of optoelectronics and photovoltaics. In recent years, perovskites have gained considerable attention as an inexpensive and easy-to-synthesize light absorbing material for so-called organic-inorganic solar cells. In this study we wish to examine the structural and electronic properties of CH3NH3PbI3 organohalide lead perovskites. Charge transport behaviour between the light harvesting perovskite and the underlying electron transport mesostructure are some of the factors that affect the Power Conversion Efficiencies (PCE) of these devices. Therefore, advanced characterization methods were used to investigate the structural and electronic changes that may occur at the interface. Scanning electron microscopy (SEM) was used to survey the structure and morphology of the samples. It was found that the titania grain sizes were 20-25 nm in size and the perovskite grain sizes from 200 nm to 500 nm. The samples were prepared using a solution processing method, which is widely considered as one of the most cost effective ways for crystal growth. However, our studies show that this method does not provide a full perovskite coverage of the surface (14.4% of surface uncovered) which reduces the light harvesting yield. X-ray diffraction (XRD) was employed to study the crystal structure of the sample. It was concluded that the titania was in the anatase phase and the perovskite in a tetragonal crystal system (space group: I4/mcm), with a cell size of a=8.89 A and c=12.68 A. Moreover, our XRD results reveal the existence of a PbI2 crystal phase, indicating an incomplete conversion of the precursors to the perovskite phase. In order to probe the changes that occur at the interface and to elucidate the electron transport mechanisms, X-ray photoelectron spectroscopy (XPS) was conducted and the core-level spectra was investigated. A shift of 0.44 eV in the binding energy of the Ti 2p line was observed between the titania samples and the titania/perovskite. We hypothesize the origin of this shift to be due to a local screening effect, or the formation of a barrier between the perovskite and the titania that is hindering charge transport and is preventing the compensation for the surface charges lost during photoionization. Based on the findings presented in this thesis we suggest, as a possible research direction for the future, UV Photoelectron Spectroscopy (UPS) for constructing the band alignment schemes with the PbI2 layer included and a thorough investigation of the substrate effects and the synthesis routes on the charge transport dynamics of these systems.