Fluorescence intermittency is a random switching between emitting (on) and non-emitting (off) periods found for many single chromophores such as semiconductor quantum dots and organic molecules. The statistics of the duration of on- and off-periods are commonly determined by thresholding the emission time trace of a single chromophore and appear to be power law distributed. Here we test with the help of simulations if the experimentally determined power law distributions can actually reflect the underlying statistics. We find that with the experimentally limited time resolution real power law statistics with exponents αon/off ≳ 1.6, especially if αon ≠ αoff would not be observed as such in the experimental data after binning and thresholding. Instead, a power law appearance could simply be obtained from the continuous distribution of intermediate intensity levels. This challenges much of the obtained data and the models describing the so-called power law blinking.

Our model considers a new element in forest fire modeling, namely the dynamics of a forest animal, intimately linked to the trees. We show that animals and trees react differently to different types of fire. A high probability of fire initiation results in several small fires, which do not allow for a large fuel accumulation and thus the destruction of many trees by fire, but is found to be generally devastating to the animal population at the same time. On the other hand, a low fire initiation probability allows for the accumulation of higher quantities of fuel, which in turn results in larger fires, more devastating to the trees than to the animals. Thus, we suggest that optimal fire management should take into account the relation between fire initiation and its different effects on animals and trees. Further, wildfires are often considered as prime examples for power-law-like frequency distributions, yet there is no agreement on the mechanisms responsible for the observed patterns. Our model suggests that instead of a single unified distribution, a superposition of at least two different distributions can be detected and this suggests multiform mechanisms acting on different scales. None of the discovered distributions are compatible with the power-law hypothesis.

Ecosystems provide important functioning and services, like biomass for bioenergy production or storage of atmospheric carbon. Two examples of such ecosystems are temperate grasslands and tropical forests. Both vegetation are rich of various species, whereby each of the respective ecosystem benefits from its species-richness concerning their functioning, i.e. productivity. In this thesis both vegetation are in the focus of the investigations. In the first chapter, a review of existing grassland and vegetation models provides an overview of important aspects, which have to be considered for modelling temperate grasslands in the context of biomass production. Based on the review, new conceptual modelling approaches for temperate grasslands are proposed. In the third chapter, derived from the suggested concept, the process-oriented and individual-based grassland model Grassmind is presented. In the fourth chapter, the model Grassmind is used in order to parameterize and simulate the annual dynamics of a typical Central European grass species. Grassmind is able to reproduce the structure and dynamics of a temperate grass species. With reference to the parameterized grass species, a simulation study using defined species groups is performed in order to investigate on the effect of the richness of species groups on aboveground productivity. We do not observe a significant positive effect of species group richness on productivity, which is explained by limitations of using the parameterized grass species as a reference. In the fifth chapter, comprehensive investigations are carried out on the example of stem size distributions in forests concerning their statistical analyses, i.e. by using maximum likelihood estimation. The effects of uncertainties, i.e. binning of measured stem sizes or random measurement errors, are examined in detail. Uncertainties bias the analyses of maximum likelihood estimations. It is shown, that the use of modified likelihood functions, which include either binning or measurement errors, reduce these biases to a large extent. For both studies, i.e. modelling of temperate grasslands and analysing stem size distributions of forests, the presented investigations are discussed and possible examinations are suggested for future research in the last chapter.

Analytic functions in a domain Ω are uniquely determined by their values on any curve Γ ⊂ Ω. We provide sharp quantitative version of this statement. Namely, let f be of order E on Γ relative to its global size in Ω (measured in some Hilbert space norm). How large can f be at a point z away from the curve? We give a sharp upper bound on |f(z)| in terms of a solution of a linear integral equation of Fredholm type and demonstrate that the bound behaves like a power law: E^γ(z). In special geometries, such as the upper halfplane, annulus or ellipse the integral equation can be solved explicitly, giving exact formulas for the optimal exponent γ(z). Our methods can be applied to non-Hilbertian settings as well. Further, we apply the developed theory to study the degree of reliability of extrapolation of the complex electromagentic permittivity function based on its analyticity properties. Given two analytic functions, representing extrapolants of the same experimental data, we quantify how much they can differ at an extrapolation point outside of the experimentally accessible frequency band.

It has been observed that real-world random networks like the WWW, Internet, social networks, citation networks, etc., organize themselves into closely-knit groups that are locally dense and globally sparse. These closely-knit groups are termed communities. Nodes within a community are similar in some aspect. For example in a WWW network, communities might consist of web pages that share similar contents. Mining these communities facilitates better understanding of their evolution and topology, and is of great theoretical and commercial significance. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network, whereas community identification is the problem of identifying the community, to which, a given set of nodes belong. We make a comparative study of various existing community-discovery algorithms. We then propose a new algorithm based on bibliographic metrics, which addresses the drawbacks in existing approaches. Bibliographic metrics are used to study similarities between publications in a citation network. Our algorithm classifies nodes in the network based on the similarity of their neighborhoods. One of the drawbacks of the current community-discovery algorithms is their computational complexity. These algorithms do not scale up to the enormous size of the real-world networks. We propose a hash-table-based technique that helps us compute the bibliometric similarity between nodes in O(m ?) time. Here m is the number of edges in the graph and ?, the largest degree. Next, we investigate different centrality metrics. Centrality metrics are used to portray the importance of a node in the network. We propose an algorithm that utilizes centrality metrics of the nodes to compute the importance of the edges in the network. Removal of the edges in ascending order of their importance breaks the network into components, each of which represent a community. We compare the performance of the algorithm on synthetic networks with a known community structure using several centrality metrics. Performance was measured as the percentage of nodes that were correctly classified. As an illustration, we model the ucf.edu domain as a web graph and analyze the changes in its properties like densification power law, edge density, degree distribution, diameter, etc., over a five-year period. Our results show super-linear growth in the number of edges with time. We observe (and explain) that despite the increase in average degree of the nodes, the edge density decreases with time.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24740号 / 情博第828号 / 新制||情||139(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 梅野 健, 教授 山下 信雄, 准教授 加嶋 健司 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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<p> This dissertation consists of two topics. In chapter 1, we develop a discrete disaggregated model in which, the market maker can observe individual order flow instead of a batch order in Kyle (1985). The model suggests that the behavior of the uninformed traders play an important role in how the informed make the optimal trading strategy : when the uninformed is more likely to use large order, the informed will also trade large, no matter what size of signal he receives, and when the uninformed tend to trade with small size order, the informed will have to trade small quantity to maximize his expected profit, even if he receives the large value signal. When the uninformed does not prefer size of order, the informed will trade smaller (larger) quantities when receiving small(large) value signals. The result is consistent with the behavior of the informed in Kyle (1985). We further investigate order flow disaggregation on market liquidity by comparing aggregated order flow structure, in which market maker observes aggregated order flow. When the model setup is symmetric, the aggregated structure can provide more liquidity, while the disaggregated structure is more liquid under the asymmetric model setup. In chapter 2, we employ the type 2 joint power law distribution in Mardia (1962) to study the joint effect of the return and trading volume. The parameter estimate for marginal distribution in joint power-law exhibits the same pattern as in univariate power law literature for return and volume, but the value are smaller due to the joint effect of return and trading volume. However, we find the joint power law shows higher predictability than the univariate power law by employing the measure MSE (Means squared error). Additionally, the type 2 joint power law indicates the linear relationship between log absolute value of return and log trading volume , which suggests the none linear impact of trading volume on price. We also find that, as sampling interval shrinks from day to 15 seconds, the price impact will increase. And also as the waiting time for two consecutive transactions shrinks, the price impact will increase, which is in line with the result of Dufour and Engle (2000). </p>

Purpose/Aim: To find power structures within the blog network. Material/Method: Using keywords to find all available blog posts about the National Defence Radio Establishment from the blog search engine Twingly, and thereafter using the same blog search engine to find inlinks from other blogs, to those posts. The data is set into the context of the small-world networks models of Duncan J. Watts and rich-club models of Sergi Valverde och Ricard V. Sole. Main results: 5183 unique blogs have written about the subject in 22779 blog posts to which 28128 inlinks from other blogposts are made. Just over one fifth of the blogs are linkted to each other in one big network, where the remaining blogs stand without any ingoing or outgoing links. The first bloggers are the one who continue to write for longer period of time and also the ones who attracts most inlinks. The blogosphere around this subject is highly connected, shows features as one would find in a small-world network, displays a power-law distribution for inlinks and is highly clustered around a few rich- club nodes.