Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.

The subject of this thesis is searching in unstructured peer-to-peer systems. Such systems have been used for a variety of different applications, including file-sharing, content distribution and video streaming. These applications have been very popular; they contribute to a large percentage of today's Internet traffic and their users typically number in the millions. By searching, we refer to the process of locating content stored by peers. Searching in unstructured peer-to-peer systems poses a challenge because of high churn: both the topology and the content stored by peers can change quickly as peers arrive and depart, while the network formed under this churn process can be arbitrary at any point in time. As a result, a search mechanism must operate without any a priori assumptions on this dynamic topology. Ideally, a search mechanism should be scalable: as, typically, peers have limited bandwidth, the traffic generated by queries should not grow significantly as the peer population increases. Moreover, a search mechanism should also be reliable: if certain content is in the system, searching should locate it with reasonable guarantees. These two goals can be conflicting, as generating more queries increases a mechanism's reliability but decreases its scalability. Hence, a fundamental question regarding searching in unstructured systems is whether a mechanism can exhibit both properties, despite the network's dynamic and arbitrary nature. In this thesis, we show this is indeed the case, by proposing a novel mechanism that is both scalable and reliable. This is shown under a mathematical model that captures the evolution of both network and content in an unstructured system, but is also verified through simulations. To the best of our knowledge, this is the first provably scalable and reliable search mechanism for unstructured peer-to-peer systems. In addition to the above problem, we also consider a hybrid peer-to-peer system, in which the peer-to-peer network co-exists with a central server. The purpose of this hybrid architecture is to reduce the server's traffic by delegating part of it to its clients ---\emph{i.e.}, the peers: a peer wishing to retrieve certain content first propagates a query over the peer-to-peer network, and downloads the content from the server only if the query fails. This hybrid architecture can be used to partially decentralize a content distribution server, a search engine, an online encyclopedia, etc. The trade-off between scalability and reliability translates, in the hybrid case, to a trade-off between the peer and the server traffic loads. We propose a search mechanism under which both loads remain bounded as the peer population grows. This is surprising, and has an important implication: one can construct hybrid peer-to-peer systems that can handle traffic generated by a large (unbounded) peer population, even when both the server and peer bandwidth capacities are limited. Again, this is proved under a model capturing the hybrid system's dynamic nature and verified through simulations. To the best of our knowledge, our work is the first to show that hybrid systems with such properties exist.

The subject of this thesis is searching in unstructured peer-to-peer systems. Such systems have been used for a variety of different applications, including file-sharing, content distribution and video streaming. These applications have been very popular; they contribute to a large percentage of today's Internet traffic and their users typically number in the millions. By searching, we refer to the process of locating content stored by peers. Searching in unstructured peer-to-peer systems poses a challenge because of high churn: both the topology and the content stored by peers can change quickly as peers arrive and depart, while the network formed under this churn process can be arbitrary at any point in time. As a result, a search mechanism must operate without any a priori assumptions on this dynamic topology. Ideally, a search mechanism should be scalable: as, typically, peers have limited bandwidth, the traffic generated by queries should not grow significantly as the peer population increases. Moreover, a search mechanism should also be reliable: if certain content is in the system, searching should locate it with reasonable guarantees. These two goals can be conflicting, as generating more queries increases a mechanism's reliability but decreases its scalability. Hence, a fundamental question regarding searching in unstructured systems is whether a mechanism can exhibit both properties, despite the network's dynamic and arbitrary nature. In this thesis, we show this is indeed the case, by proposing a novel mechanism that is both scalable and reliable. This is shown under a mathematical model that captures the evolution of both network and content in an unstructured system, but is also verified through simulations. To the best of our knowledge, this is the first provably scalable and reliable search mechanism for unstructured peer-to-peer systems. In addition to the above problem, we also consider a hybrid peer-to-peer system, in which the peer-to-peer network co-exists with a central server. The purpose of this hybrid architecture is to reduce the server's traffic by delegating part of it to its clients ---\emph{i.e.}, the peers: a peer wishing to retrieve certain content first propagates a query over the peer-to-peer network, and downloads the content from the server only if the query fails. This hybrid architecture can be used to partially decentralize a content distribution server, a search engine, an online encyclopedia, etc. The trade-off between scalability and reliability translates, in the hybrid case, to a trade-off between the peer and the server traffic loads. We propose a search mechanism under which both loads remain bounded as the peer population grows. This is surprising, and has an important implication: one can construct hybrid peer-to-peer systems that can handle traffic generated by a large (unbounded) peer population, even when both the server and peer bandwidth capacities are limited. Again, this is proved under a model capturing the hybrid system's dynamic nature and verified through simulations. To the best of our knowledge, our work is the first to show that hybrid systems with such properties exist.

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Syftet med denna uppsats är att undersöka två monetära modellers prognosförmåga för den svenska kronan. Detta är den första studie som utvärderar prognoser på den svenska kronan under rörlig växelkurs. Modellerna som används är ”flexible price monetary model” samt ”sticky price monetary model”. Modellerna jämförs dels med en random walk-modell, men även mot varandra för att kunna påvisa eventuella skillnader modellerna emellan. För att utreda om det finns olika förklaringsvärde i modellerna beroende på referensvalutan har jag använt mig av två olika växelkurspar, nämligen SEK/EUR och SEK/GBP. Resultaten tyder på att en trögrörlig monetär modell för växelkursparet SEK/EUR lyckas slå en random walk på lite längre sikt, även om resultatet bör tolkas med viss försiktighet. Det verkar även som att det har stor betydelse vilken referensvaluta man använder sig av då resultaten växelkursparen emellan skiljer sig åt ganska kraftigt.

Animal movement patterns provide a rich source of information for examining a wide range of ecological interactions that span ecological scales from foraging behaviors of individuals to the spread of populations across landscapes. I investigated the causes and consequences of consumer movement, from the localized movements of individuals to the patterns of spread of populations across landscapes, using a series of complimentary microcosm experiments with a model consumer-resource system. In chapter one, I conducted a series of experiments designed to test differences in the fine-scale movement characteristics of swimming rotifers under experimental manipulations of local resource and conspecific abundance. Individual turn frequencies increased in resource-rich environments but were unaffected by competitor density. In contrast, individual swimming speeds increased at high competitor densities but were unaffected by resources. I demonstrated how these contrasting behaviors could be integrated to form predictions of population spread under different ecological scenarios. In chapter two, I tested the predictions established in chapter one by directly measuring the rates of spread of many replicate populations of rotifers in one-dimensional environments. Experimental treatments included a wide range of resource and conspecific densities, and starved versus sated rotifers in the presence versus absence of predator chemical cues. Rates of population spread were negatively correlated with resource abundance, especially when conspecific density was high, and rates of spread of both starved and risk-exposed populations were significantly lower than controls. In chapter three, I tested the effect of resource patchiness, conspecific density, and their interaction, on population spread through a two dimensional landscape. I found that rates of population spread decayed over time indicative of a sub-diffusive movement processes explained by positive density-dependent movement responses. Neither the rate of spread nor the magnitude of its decay differed between patchy and evenly distributed resource treatments, despite observed rotifer preferences for patches. These findings suggest that under certain ecological circumstances resource distribution may be less crucial in predicting population spread than density-dependence. Overall, my research demonstrates mechanistic links between the behavioural responses of individuals to their environment and the resulting larger scale phenomena of population-level movement patterns.

Nanocrystalline materials are polycrystalline solids with grain size in the nanometer range (< 100nm), which have been found to exhibit superior properties such as high magnetic permeability and corrosion resistance, as well as a considerably increase of strength when compared with their coarse grain counterparts. All those improved properties are attributed to the high volume fraction of grain boundaries (GBs). However, the high density of GBs brings a large amount of excess enthalpy to the whole system, making the nanostructures unstable and suffer from severe thermal or mechanical grain growth. In order to maintain the advantageous properties of nanocrystalline materials, it is necessary to stabilize GB and inhibit grain growth. While alloying has been found to be an effective way of achieving stabilized nanocrystalline metal alloys experimentally, the direct quantification of solute effects on GB motion still poses great challenge for investigating thermal stability of general nanocrystalline materials. In this research, impurity segregation and solute drag effects on GB motion were investigated by extending the interface random-walk method in direct molecular dynamics simulations. It was found that the GB motion was controlled by the solute diffusion perpendicular to the boundary plane. Based on the simulation results at different temperatures and impurity concentrations, the solute drag effects can be well modeled by the theory proposed by Cahn, Lücke and Stüwe (CLS model) more than fifty years ago. However, a correction to the original CLS model needs to be made in order to quantitatively predict the solute drag effects on a moving GB.

Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.

This paper surveys various statistical methods that have been proposed for the examination of the efficiency of financial markets and proposes a novel procedure for testing the predictability of a time series. For illustration, this procedure is applied to Austrian stock return series.