<div> Interference management is necessary to meet the growth in demand for wireless data services. The problem was studied in previous work by assuming a fixed channel connectivity model, while network topologies tend to change frequently in practice. </div><div><br></div><div>The associations between cell edge mobile terminals and base stations in a wireless interference network that is backed by cooperative communication schemes is investigated and association decisions are identified that are information-theoretically optimal when taking the uplink-downlink average. Then, linear wireless networks are evaluated from a statistical point of view, where the associations between base stations and mobile terminals are fixed and channel fluctuations exist due to shadow fading. Moreover, the considered fading model is formed by having links in the wireless network, each subject independently to erasure with a known probability. </div><div><br></div><div>Throughout the information theoretic analysis, it is assumed that the network topology is known to the cooperating transmitting nodes. This assumption may not hold in practical wireless networks, particularly Ad-Hoc ones, where decentralized mobile nodes form a temporary network. Further, communication in many next generation networks, including cellular, is envisioned to take place over different wireless technologies, similar to the co-existence of Bluetooth, ZigBee, and WiFi in the 2.4 GHz ISM-Band. The competition of these wireless technologies for scarce spectrum resources confines their coexistence. It is hence elementary for collaborative interference management strategies to identify the channel type and index of a wireless signal, that is received, to promote intelligent use of available frequency bands. It is shown that deep learning based approaches can be used to identify interference between the wireless technologies of the 2.4 GHz ISM-Band effectively, which is compulsory for identifying the channel topology. The value of using deep neural network architectures such as CNN, CLDNN, LSTM, ResNet and DenseNet for this problem of Wireless Channel Identification is investigated. Here, the major focus is on minimizing the time, that takes for training, and keeping a high classification accuracy of the different network architectures through band and training SNR selection, Principal Component Analysis (PCA) and different sub-Nyquist sampling techniques. </div><div>Finally, a number theoretic approach for fast discovery of the network topology is proposed. More precisely, partial results on the simulation of the message passing model are utilized to present a model for discovering the network topology. Specifically, the minimum number of communication rounds needed to discover the network topology is examined. Here, a single-hop network is considered that is restricted to interference-avoidance, i.e., a message is successfully delivered if and only if the transmitting node is the only active transmitter connected to its receiving node. Then, the interference avoidance restriction is relaxed by assuming that receivers can eliminate interference emanating from already discovered transmitters. Finally, it is explored how the network size and the number of interfering transmitters per user adjust the sum of observations.</div><div><br></div>

This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.

This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.

Dynamical structure functions were developed as a partial structure representation of linear time-invariant systems to be used in the reconstruction of biological networks. Dynamical structure functions contain more information about structure than a system's transfer function, while requiring less a priori information for reconstruction than the complete computational structure associated with the state space realization. Early sufficient conditions for network reconstruction with dynamical structure functions severely restricted the possible applications of the reconstruction process to networks where each input independently controls a measured state. The first contribution of this thesis is to extend the previously established sufficient conditions to incorporate both necessary and sufficient conditions for reconstruction. These new conditions allow for the reconstruction of a larger number of networks, even networks where independent control of measured states is not possible. The second contribution of this thesis is to extend the robust reconstruction algorithm to all reconstructible networks. This extension is important because it allows for the reconstruction of networks from real data, where noise is present in the measurements of the system. The third contribution of this thesis is a Matlab toolbox that implements the robust reconstruction algorithm discussed above. The Matlab toolbox takes in input-output data from simulations or real-life perturbation experiments and returns the proposed Boolean structure of the network. The final contribution of this thesis is to increase the applicability of dynamical structure functions to more than just biological networks by applying our reconstruction method to wireless communication networks. The reconstruction of wireless networks produces a dynamic interference map that can be used to improve network performance or interpret changes of link rates in terms of changes in network structure, enabling novel anomaly detection and security schemes.