It is well known that the group completion of the classifying space of the free permutative category is Ω∞ S∞, i.e. stable homotopy of the 0-sphere. Quillen´s S-1S construction can be applied to the free permutative category, which has a pictorial description by pseudo-tangles, and this leads to another pictorial descripted category G which has the classifying space Ω∞ S∞. With help of this model G we can give generators for the homotopy groups of Ω∞ S∞ for i=0,1,2. As a further application, we compute the fundamental group of the free permutative category with duality and show that the association of a duality structure on the categorial level does not lead to a group completion on the level of classifying spaces.

In this thesis an optimal stopping problem related to the classical secretary problem is studied. The theory of optimal stopping represents a special branch of stochastic optimization. Here the socalled full information best choice problem with a known number of offers is generalized by maximizing the probability of selecting an r-candidate, where an offer is called r-candidate if it is not lower than the maximal offer reduced by function r. In the first part discrete time is investigated. For this optimal stopping problem to select an r-candidate an optimal stopping time is indicated, the suboptimal myopic stopping time is displayed and threshold rules are studied including asymptotic behaviour. The basis of this optimal stopping problem is displayed in a general setting where the payoff depends on the prophet´s choiceand on the maximal offer, i.e. the value of the prophet. As a further application the mean of the ratio of the gambler´s choice and prophet´s value is investigated. Then in the second part offers arrive in continuous time. Offers are presented according to random arrival times and the horizon terminating the period of choosing is taken to be fixed and random. Here stress is layed on the geometric and on the exponential distribution, i.e. the Poisson process. In the final part the optimal stopping problem of maximizing the duration of owning a sufficiently good offer is applied to the concept of an r-candidate. A distinction between an overall and a temporary r-candidate is made. The duration of owning an r-candidate is investigated for a finite number of offers with regard to recall. The duration problem with discounted epochs is resolved. Finally the duration of owning an r-candidate is considered regarding the Poisson process where the horizon is fixed and exponentially distributed.

In this work, we investigate job-shop problems where limited capacity buffers to store jobs in non-processing periods are present. In such a problem setting, after finishing processing on a machine, a job either directly has to be processed on the following machine or it has to be stored in a prespecified buffer. If the buffer is completely occupied the job may wait on its current machine but blocks this machine for other jobs. Besides a general buffer model,also specific configurations are considered.The key issue to develop fast heuristics for the job-shop problem with buffers is to find a compact representation of solutions. In contrast to the classical job-shop problem,where a solution may be given by the sequences of the jobs on the machines, now also the buffers have to be incorporated in the solution representation. In this work, we propose two solution representations for the job-shop problem with buffers. Furthermore, we investigate whether the given solution representations can be simplified for specific buffer configurations. For the general buffer configuration it is shown that an incorporation of the buffers in the solution representation is necessary, whereas for specific buffer configurations possible simplifications are presented. Based on the given solution representations we develop local search heuristics in the second part of this work. Therefore, the well-known block approach for the classical job-shop problem is generalized to the job-shop problem with specific buffer configurations.

A very general framework for modeling uncertainty in learning environments is given by Partially Observable Markov Decision Processes (POMDPs). In a POMDP setting, the learning agent infers a policy for acting optimally in all possible states of the environment, while receiving only observations of these states. The basic idea for coping with partial observability is to include memory into the representation of the policy. Perfect memory is provided by the belief space, i.e. the space of probability distributions over environmental states. However, computing policies defined on the belief space requires a considerable amount of prior knowledge about the learning problem and is expensive in terms of computation time. In this thesis, we present a reinforcement learning algorithm for solving deterministic POMDPs based on short-term memory. Short-term memory is implemented by sequences of past observations and actions which are called history lists. In contrast to belief states, history lists are not capable of representing optimal policies, but are far more practical and require no prior knowledge about the learning problem. The algorithm presented learns policies consisting of two separate phases. During the first phase, the learning agent collects information by actively establishing a history list identifying the current state. This phase is called the efficient identification strategy. After the current state has been determined, the Q-Learning algorithm is used to learn a near optimal policy. We show that such a procedure can be also used to solve large Markov Decision Processes (MDPs). Solving MDPs with continuous, multi-dimensional state spaces requires some form of abstraction over states. One particular way of establishing such abstraction is to ignore the original state information, only considering features of states. This form of state abstraction is closely related to POMDPs, since features of states can be interpreted as observations of states.

(I) Background. Conflicts emerge when populations of protected species grow to sizes that cause noticeable economic damage - like in the case of the fish consuming Great Cormorant (Phalacrocorax carbo sinensis). One possible approach for reconciliation is to regulate the size of the population in question. In doing so, regulation strategies have to meet multiple targets: 1) population size has to be reduced; 2) the viability of the population has to be maintained; 3) strategies have to adhere to the available budget. This thesis focuses on the regulation of populations that are structured into two groups - breeders and mature non-breeders. The pool of non-breeders provides a reserve for the breeders, whereby they may enable the population to resist regulation attempts. (II) Aims. 1) Development of a modeling framework and a conceptual model to provide an understanding of the functioning and effect of the population structure induced by non-breeders on population dynamics in a fluctuating environment. 2) Uncover the relation between non-breeder characteristics and the performance of regulation strategies. 3) Application of the modeling approach to the regulation of the Cormorant in order to evaluate the results from the conceptual model and find statements to support decisions on management strategies. (III) Methods. A conceptual stochastic time-discrete model, based on the logistic map with overlapping generations, is developed. Different types of threshold regulation strategies are applied. Strategies differed in which part of the model was affected by regulation. Resulting rules from the conceptual model are tested by applying them to a second age-structured model of a cormorant population, parametrized with data gained from a cormorant colony in Denmark. Analyzes of this model focus on the ecological-economic performance of regulation strategies and result in rankings of regulation options. Regulation performance is judged from different economic perspectives.

Robustness and adaptivity are important behavioural properties observed in biological systems, which are still widely absent in artificial intelligence applications. Such static or non-plastic artificial systems are limited to their very specific problem domain. This work introducesa general model for synaptic plasticity in embedded artificial recurrent neural networks, which is related to short-term plasticity by synaptic scaling in biological systems. The model is general in the sense that is does not require trigger mechanisms or artificial limitations and it operates on recurrent neural networks of arbitrary structure. A Self-Regulation Neuron is defined as a homeostatic unit which regulates its activity against external disturbances towards a target value by modulation of its incoming and outgoing synapses. Embedded and situated in the sensori-motor loop, a network of these neurons is permanently driven by external stimuli andwill generally not settle at its asymptotically stable state. The system´s behaviour is determinedby the local interactions of the Self-Regulating Neurons. The neuron model is analysed as a dynamical system with respect to its attractor landscape and its transient dynamics. The latter is conducted based on different control structures for obstacle avoidance with increasing structural complexity derived from literature. The result isa controller that shows first traces of adaptivity. Next, two controllers for different tasks are evolved and their transient dynamics are fully analysed. The results of this work not only show that the proposed neuron model enhances the behavioural properties, but also points out the limitations of short-term plasticity which does not account for learning and memory.

Simulation von Federmassenschwingern

Our symposium will bring together experts from the German and international 'Inverse Problems Community' and young scientists. The focus will be on ill-posedness phenomena, regularization theory and practice, and on the analytical, numerical, and stochastic treatment of applied inverse problems in natural sciences, engineering, and finance.

We are investigating a kernel-based autoconvolution problem, which has its origin in the physics of ultra short laser pulses. The task in this problem is to reconstruct a complex-valued function $x$ on a finite interval from measurements of its absolute value and a kernel-based autoconvolution of the form [[F(x)](s)=int k(s,t)x(s-t)x(t)de t.] This problem has not been studied in the literature. One reason might be that one has more information than in the classical autoconvolution case, where only the right hand side is available. Nevertheless we show that ill posedness phenomena may occur. We also propose an algorithm to solve the problem numerically and demonstrate its performance with artificial data. Since the algorithm fails to produce good results with real data and we suspect that the data for $|F(x)|$ are not dependable we also consider the whole problem with only $arg(F(x))$ given instead of $F(x)$.

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