A large number of complex systems can be modelled as networks of interacting units. From a mathematical point of view the topology of such systems can be represented as graphs of which the nodes represent individual elements of the system and the edges interactions or relations between them. In recent years networks have become a principal tool for analyzing complex systems in many different fields. This thesis introduces an information theoretic approach for finding characteristic connectivity patterns of networks, also called network motifs. Network motifs are sometimes also referred to as basic building blocks of complex networks. Many real world networks contain a statistically surprising number of certain subgraph patterns called network motifs. In biological and technological networks motifs are thought to contribute to the overall function of the network by performing modular tasks such as information processing. Therefore, methods for identifying network motifs are of great scientific interest. In the prevalent approach to motif analysis network motifs are defined to be subgraphs that occur significantly more often in a network when compared to a null model that preserves certain features of the network. However, defining appropriate null models and sampling these has proven to be challenging. This thesis introduces an alternative approach to motif analysis which looks at motifs as regularities of a network that can be exploited to obtain a more efficient representation of the network. The approach is based on finding a subgraph cover that represents the network using minimal total information. Here, a subgraph cover is a set of subgraphs such that every edge of the graph is contained in at least one subgraph in the cover while the total information of a subgraph cover is the information required to specify the connectivity patterns occurring in the cover together with their position in the graph. The thesis also studies the connection between motif analysis and random graph models for networks. Developing random graph models that incorporate high densities of triangles and other motifs has long been a goal of network research. In recent years, two such model have been proposed . However, their applications have remained limited because of the lack of a method for fitting such models to networks. In this thesis, we address this problem by showing that these models can be formulated as ensembles of subgraph covers and that the total information optimal subgraph covers can be used to match networks with such models. Moreover, these models can be solved analytically for many of their properties allowing for more accurate modelling of networks in general. Finally, the thesis also analyzes the problem of finding a total information optimal subgraph cover with respect to its computational complexity. The problem turns out to be NP-hard hence, we propose a greedy heuristic for it. Empirical results for several real world networks from different fields are presented. In order to test the presented algorithm we also consider some synthetic networks with predetermined motif structure.

Genealogy reconstruction is widely used in biology when relationships among entities are studied. Phylogenies, or evolutionary trees, show the differences between species. They are of profound importance because they help to obtain better understandings of evolutionary processes. Pedigrees, or family trees, on the other hand visualize the relatedness between individuals in a population. The reconstruction of pedigrees and the inference of parentage in general is now a cornerstone in molecular ecology. Applications include the direct infer- ence of gene flow, estimation of the effective population size and parameters describing the population’s mating behaviour such as rates of inbreeding. In the first part of this thesis, we construct genealogies of various types of cancer. Histopatho- logical classification of human tumors relies in part on the degree of differentiation of the tumor sample. To date, there is no objective systematic method to categorize tumor subtypes by maturation. We introduce a novel algorithm to rank tumor subtypes according to the dis- similarity of their gene expression from that of stem cells and fully differentiated tissue, and thereby construct a phylogenetic tree of cancer. We validate our methodology with expression data of leukemia and liposarcoma subtypes and then apply it to a broader group of sarcomas and of breast cancer subtypes. This ranking of tumor subtypes resulting from the application of our methodology allows the identification of genes correlated with differentiation and may help to identify novel therapeutic targets. Our algorithm represents the first phylogeny-based tool to analyze the differentiation status of human tumors. In contrast to asexually reproducing cancer cell populations, pedigrees of sexually reproduc- ing populations cannot be represented by phylogenetic trees. Pedigrees are directed acyclic graphs (DAGs) and therefore resemble more phylogenetic networks where reticulate events are indicated by vertices with two incoming arcs. We present a software package for pedigree reconstruction in natural populations using co-dominant genomic markers such as microsatel- lites and single nucleotide polymorphism (SNPs) in the second part of the thesis. If available, the algorithm makes use of prior information such as known relationships (sub-pedigrees) or the age and sex of individuals. Statistical confidence is estimated by Markov chain Monte Carlo (MCMC) sampling. The accuracy of the algorithm is demonstrated for simulated data as well as an empirical data set with known pedigree. The parentage inference is robust even in the presence of genotyping errors. We further demonstrate the accuracy of the algorithm on simulated clonal populations. We show that the joint estimation of parameters of inter- est such as the rate of self-fertilization or clonality is possible with high accuracy even with marker panels of moderate power. Classical methods can only assign a very limited number of statistically significant parentages in this case and would therefore fail. The method is implemented in a fast and easy to use open source software that scales to large datasets with many thousand individuals.

A backbone network is the central part of the communication network, which provides connectivity within the various systems across large distances. Disruptions in a backbone network would cause severe consequences which could manifest in the service outage on a large scale. Depending on the size and the importance of the network, its failure could leave a substantial impact on the area it is associated with. The failures of the network services could lead to a significant disturbance of human activities. Therefore, making backbone communication networks more resilient directly affects the resilience of the area. Contemporary urban and regional development overwhelmingly converges with the communication infrastructure expansion and their obvious mutual interconnections become more reciprocal. Spreading failures are of particular interest. They usually originate in a single network segment and then spread to the rest of network often causing a global collapse. Two types of spreading failures are given focus, namely: epidemics and cascading failures. How to make backbone networks more resilient against spreading failures? How to tune the topology or additionally protect nodes or links in order to mitigate an effect of the potential failure? Those are the main questions addressed in this thesis. First, the epidemic phenomena are discussed. The subjects of epidemic modeling and identification of the most influential spreaders are addressed using a proposed Linear Time-Invariant (LTI) system approach. Throughout the years, LTI system theory has been used mostly to describe electrical circuits and networks. LTI is suitable to characterize the behavior of the system consisting of numerous interconnected components. The results presented in this thesis show that the same mathematical toolbox could be used for the complex network analysis. Then, cascading failures are discussed. Like any system which can be modeled using an interdependence graph with limited capacity of either nodes or edges, backbone networks are prone to cascades. Numerical simulations are used to model such failures. The resilience of European National Research and Education Networks (NREN) is assessed, weak points and critical areas of the network are identified and the suggestions for its modification are proposed.

The central theme of complex systems research is to understand the emergent macroscopic properties of a system from the interplay of its microscopic constituents. The emergence of macroscopic properties is often intimately related to the structure of the microscopic interactions. Here, we present an analytical approach for deriving necessary conditions that an interaction network has to obey in order to support a given type of macroscopic behaviour. The approach is based on a graphical notation, which allows rewriting Jacobi’s signature criterion in an interpretable form and which can be applied to many systems of symmetrically coupled units. The derived conditions pertain to structures on all scales, ranging from individual nodes to the interaction network as a whole. For the purpose of illustration, we consider the example of synchronization, specifically the (heterogeneous) Kuramoto model and an adaptive variant. The results complete and extend the previous analysis of Do et al. (2012 Phys. Rev. Lett. 108, 194102).

Routing in Disruption-Tolerant Networks has been researched for over 15 years. Several proposed algorithms exploit the predictive behavior of mobile devices in order to maximize a desired metric (e.g., delivery probability) and minimize waste of resources. However, even devices that follow a highly predictive mobility model might have its behavior temporarily altered due to external events such as accidents, natural conditions, mechanical failures, etc. Some routing approaches for predictive networks are not able to make use of the available knowledge to support the routing decision. Others are not able to adapt under context change. In this work, we present the initial phase of our research and the necessary steps towards an adaptive DTN protocol for challenging networks that is able to exploit available knowledge and adapt under context changes.:I. Introduction II. Challenging Networks III. Challenges Towards an Adaptive Framework IV. Framework Design and Implementation V. Conclusion

Modeling complex gene interacting systems as Boolean networks lead to a significant simplification of computational investigation. This can be achieved by discretization of the expression level to ON or OFF states and classifying the interactions to inhibitory and activating. In this respect, Boolean functions are responsible for the evolution of the binary elements of the Boolean networks. In this thesis, we investigate the mostly used Boolean functions in modeling gene regulatory networks. Moreover, we introduce a new type of function with strong inhibitory namely the veto function. Our computational and analytic studies on the verity of the networks capable of constructing the same State Transition Graph lead to define a new concept namely the “degeneracy” of Boolean functions. We further derive analytically the sensitivity of the Boolean functions to perturbations. It turns out that the veto function forms the most robust dynamics. Furthermore, we verify the applicability of veto function to model the yeast cell cycle networks. In particular, we show that in an intracellular signal transduction network [Helikar et al, PNAS (2008)], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. The statistics of the connections of the functional networks are studied in detail. Finally, we look at a different scale of biological phenomena using a binary model. We propose a simple correlation-based model to describe the pattern formation of Fly eye. Specifically, we model two different procedures of Fly eye formation, and provide a generic approach for Fly eye simulation.

Optimized implementations of blocking and nonblocking collective operations are most important for scalable high-performance applications. Offloading such collective operations into the communication layer can improve performance and asynchronous progression of the operations. However, it is most important that such offloading schemes remain flexible in order to support user-defined (sparse neighbor) collective communications. In this work we propose a design for a collective offload unit. Our hardware design is able to execute dependency graph based representations of collective functions. To cope with the scarcity of memory resources we designed a new point to point messaging protocol which does not need to store information about unexpected messages. The offload unit proposed in this thesis could be integrated into high performance networks such as EXTOLL. Our design achieves a clock frequency of 212 MHz on a Xilinx Virtex6 FPGA, while using less than 10% of the available logic slices and less than 30% of the available memory blocks. Due to the specialization of our design we can accelerate important tasks of the message passing framework, such as message matching by a factor of two, compared to a software implementation running on a CPU with a ten times higher clock speed.:1. Task Description 1.1. Theses 2. Introduction 2.1. Motivation 2.2. Outline of this Thesis 2.3. Related Work 2.3.1. NIC Based Packet Forwarding 2.3.2. Hardware Barrier Implementations 2.3.3. ConnectX2 CORE-Direct Collective Offload Support 2.3.4. Collective Offload Support in the Portals 4 API 2.4. Group Operation Assembly Language 2.4.1. GOAL API 2.4.2. Scratchpad Buffer 2.4.3. Schedule Execution 2.5. The EXTOLL Network 2.6. Field Programmable Gate Arrays 3. Dealing with Constrained Resources 3.1. Hardware Limitations 3.2. Common Collective Functions in GOAL 3.3. Schedule Representation for the Hardware GOAL Interpreter 3.4. Executing Large Schedules using a small amount of Memory 3.4.1. Limits of Previously Suggested Approaches 3.4.2. Testing for Deadlocks in Schedules 3.4.3. Transforming Process Local Schedules into Global Schedules 3.4.4. Predetermined Buffer Locations 3.5. Queueing Active Operations in Hardware 3.6. Designing a Low-Memory-Footprint Point to Point Protocol 3.6.1. Arrival Times 3.6.2. Eager Protocol 3.6.3. Rendezvous Protocol 3.6.4. A Protocol without an Unexpected Queue 3.7. Protocol Verification 3.7.1. Capabilities of the Model Checker SPIN 3.7.2. Modeling the Protocol 3.7.3. Limitations of the Basic Protocol 4. The Matching Problem 4.1. Matching on the Host CPU 4.2. Implementation Methodology 4.3. Matching Unit Interface 4.4. Matching Unit Implementation 4.4.1. Slot Management Unit 4.4.2. The Input Consumer 4.4.3. The Output Generator 4.4.4. The Matching Unit 4.5. Slot Management Unit for Non-synchronous Transfers 5. The GOAL Interpreter 5.1. Schedule Interpreter Design 5.1.1. The Active Queue 5.1.2. The Dependency Resolver 5.2. Transceiver Interface 5.3. The Starter 5.3.1. Starting Operations 5.3.2. Processing Incoming Packets 5.3.3. Incoming Non-synchronous Packets 5.3.4. Presorting the Active Queue 5.3.5. Arbitration Units 5.3.6. IN-Filter 5.3.7. Outcommand Manager 5.3.8. Non-synchronous Protocol 5.3.9. Send Protocol 5.3.10. Receive Protocol 5.3.11. Local Operations on FPGA 6 Evaluation 6.1. Performance Analysis 6.2. Future Work 6.3. Conclusions Bibliography

Eine wachsende Anzahl von Unternehmen führt Enterprise Social Networks (ESN) ein, um den Wissensaustausch zwischen den Mitarbeitern zu verbessern und neue Möglichkeiten zur Zusammenarbeit zu schaffen. Die Anbieter von ESN-Lösungen versprechen ihren Kunden außerdem eine Erhöhung der Produktivität und Innovationskraft der Mitarbeiter. Häufig können Unternehmen diese Vorteile jedoch nicht realisieren. Gartner prognostizierte 2013, dass 80 Prozent der Unternehmen die mit ihren Social-Business-Initiativen gesteckten Ziele bis 2015 nicht erreichen werden. Zu den häufigsten Gründen für das Scheitern von ESN-Initiativen zählen fehlende Unterstützung durch die Führungskräfte, eine „inkompatible“ Unternehmenskultur, fehlende Business-Ziele sowie eine Unsicherheit in der Belegschaft, wie und wofür das neue Werkzeug genutzt werden kann. Im Vergleich zu externen sozialen Netzwerken entwickeln sich ESN häufig nicht als Selbstläufer und scheitern kurz- oder mittelfristig aufgrund mangelnder Partizipation seitens der Mitarbeiter.

Hydrogen is an appealing energy carrier for clean energy use. However, storage of hydrogen is still the main bottleneck for the realization of an energy economy based on hydrogen. Many materials with outstanding properties have been synthesized with the aim to store enough amount of hydrogen under ambient conditions. Such efforts need guidance from material science, which includes predictive theoretical tools. Carbon nanotubes were considered as promising candidates for hydrogen storage applications, but later on it was found to be unable to store enough amounts of hydrogen under ambient conditions. New arrangements of carbon nanotubes were constructed and hydrogen sorption properties were investigated using state-of-the-art simulation methods. The simulations indicate outstanding total hydrogen uptake (up to 19.0 wt.% at 77 K and 5.52wt.% at 300 K), which makes these materials excellent candidates for storage applications. This reopens the carbon route to superior materials for a hydrogen-based economy. Zeolite imidazolate frameworks are subclass of MOFs with an exceptional chemical and thermal stability. The hydrogen adsorption in ZIFs was investigated as a function of network geometry and organic linker exchange. Ab initio calculations performed at the MP2 level to obtain correct interaction energies between hydrogen molecules and the ZIF framework. Subsequently, GCMC simulations are carried out to obtain the hydrogen uptake of ZIFs at different thermodynamic conditions. The best of these materials (ZIF-8) is found to be able to store up to 5 wt.% at 77 K and high pressure. We expected possible improvement of hydrogen capacity of ZIFs by substituting the metal atom (Zn 2+) in the structure by lighter elements such as B or Li. Therefore, we investigated the energy landscape of LiB(IM)4 polymorphs in detail and analyzed their hydrogen storage capacities. The structure with the fau topology was shown to be one of the best materials for hydrogen storage. Its total hydrogen uptake at 77 K and 100 bar amounts to 7.8 wt.% comparable to the total uptake reported of MOF-177 (10 wt.%), which is a benchmark material for high pressure and low temperature H2 adsorption. Covalent organic frameworks are new class of nanoporous materials constructed solely from light elements (C, H, B, and O). The number of adsorption sites as well as the strength of adsorption are essential prerequisites for hydrogen storage in porous materials because they determine the storage capacity and the operational conditions. Currently, to the best of our knowledge, no experimental data are available on the position of preferential H2 adsorption sites in COFs. Molecular dynamics simulations were applied to determine the position of preferential hydrogen sites in COFs. Our results demonstrate that H2 molecule adsorbed at low temperature in seven different adsorption sites in COFs. The calculated adsorption energies are about 3 kJ/mol, comparable to that found for MOF systems. The gravimetric uptake for COF-108 reached 4.17 wt.% at room temperature and 100 bar, which makes this class of materials promising for hydrogen storage applications.

Endosomes are dynamic vesicular structures which transport cargo molecules internalized into the cell via endocytosis. Endosomal trafficking of cargo involves a large number of individual endosomes that regularly interact with each other via fusion and fission and thus form a dynamic network wherein endocytosed cargo is sorted and transported to various other intracellular compartments. In this study we present a general theoretical framework that takes into account individual endosomes and several key microscopic interaction processes among them. By combining theory with quantitative experiments, we seek to address the fundamental question of how the behaviour of the endosomal network emerges from the interactions among many individual endosomes of different sizes and cargo contents. Our theory is based on distributions of endosomes of various sizes and cargo amount. We compare our theory to experimental time course distributions of LDL, a degradative cargo, in a population of early endosomes. Early endosomes display a broad distribution of cargo with a characteristic power law, which we show is a consequence of stochastic fusion events of cargo carrying early endosomes. A simple model can quantitatively describe time-dependent statistics of LDL distributions in individual early endosomes. From fits of the theory to experimental data we can determine key parameters of endosomal trafficking such as the endosome fusion rate and the fluxes of cargo into and out of the network. Our theory predicts several experimentally confirmed scaling behaviours, which arise as a result of endosome fusion. Our theory provides a link between the dynamics at individual endosome level and average properties of the endosomal network. We show from our theory that some features of the endosomal distributions, which arise from interactions among individual endosomes, are sensitive to alterations in chosen parameters. This provides a direct means to study perturbation experiments wherein the cargo distribution can vary in response to changes of the endocytic system. Our analysis provides a powerful tool for the study of genetic and chemical perturbations that may alter specific systems properties and for extracting various kinetic rates involved in endosomal trafficking from only still images at different points.