This dissertation presents a computational multiscale framework for predicting behavioral tendencies related to human addiction. The research encompasses three main contributions. The first contribution presents a formal, heuristic, and exploratory framework to conduct interdisciplinary investigations about the neuropsychological, cognitive, behavioral, and recovery constituents of addiction. The second contribution proposes a computational framework to account for real-life recoveries that are not dependent on pharmaceutical, clinical, and counseling support. This exploration relies upon a combination of current biological beliefs together with unorthodox rehabilitation practices, such as meditation, and proposes a conjecture regarding possible cognitive mechanisms involved in the recovery process. Further elaboration of this investigation leads on to the third contribution, which introduces a computational hypothesis for exploring the allostatic theory of addiction. A person engaging in drug consumption is likely to encounter mood deterioration and eventually to suffer the loss of a reasonable functional state (e.g., experience depression). The allostatic theory describes how the consumption of abusive substances modifies the brain's reward system by means of two mechanisms which aim to viably maintain the functional state of an addict. The first mechanism is initiated in the reward system itself, whereas the second might originate in the endocrine system or elsewhere. The proposed computational hypothesis indicates that the first mechanism can explain the functional stabilization of the addict, whereas the second mechanism is a candidate for a source of possible recovery. The formal arguments presented in this dissertation are illustrated by simulations which delineate archetypal patterns of human behavior toward drug consumption: escalation of use and influence of conventional and alternative rehabilitation treatments. Results obtained from this computational framework encourage an integrative approach to drug rehabilitation therapies which combine conventional therapies with alternative practices to achieve higher rates of consumption cessation and lower rates of relapse.

The high-dimensional property of delay differential equations makes them useful for various purposes. The applications of systems modelled with delay differential equations demand different degrees of complexity. One solution to tune this property is to make the dynamics of the current state dependent on more delayed states. How the system responds to more delayed states depends on the system under study, as both decreases and increases in the complexity were observed in different nonlinear systems. However, it is also known that when there is an infinite number of delays that follow a continuous distribution, simpler dynamics usually expected due to the averaging over previous states that the delay kernel provides. The present thesis investigates the role of multiple delays in nonlinear time delay systems, as well as methods for evaluating their complexity. Through the use of pseudospectral differentiation, we first compute the Lyapunov exponents of such multi-delay systems. In systems with a large number of delays, chaos is found to be less likely to occur. However, in systems with oscillatory feedback functions, the entropy can increase just by adding a few delays. Our study also demonstrates that the transition to simpler dynamics in nonlinear delay systems can be either monotonous or abrupt. This is particularly true in first-order nonlinear systems, where increasing the width of the distribution of delays results in complexity collapse, even in the presence of a few discrete delays. The roots of the characteristic equation around a fixed point can be used to approximate the degree of complexity of the dynamics of such time-delay systems, as they can be linked to other dynamical invariants such as the Kolmogorov-Sinai entropy. The phenomenon of complexity collapse uncovered in our work was further studied in an 80/20 ratio excitatory-inhibitory neural network. We found that the smaller the time delay, the higher the likelihood of chaotic dynamics, and this also promotes asynchronous spiking activity. But for larger values of the delay, the neurons show synchronized oscillatory spiking activity. A global inhibition at a longer delay results in a novel dynamical pattern of randomly occurring epochs of synchrony within the chaotic dynamics. The final part of the thesis examines the behavior of time delay reservoir computing when there are multiple time delays. It is shown that the choice of spacing between time delays is crucial, and depends on the task at hand. The system was studied for a prediction task with one chaotic input as well as for a mixture of two chaotic inputs. It was found that, similar to the single delay case, there is a resonance when the difference between delays is equal to the clock cycle. Together, our research provides valuable insights into the dynamics and complexity of nonlinear multi-delay systems and the importance of the spacing between delays.

We present a theoretical study that investigates the applicability of a graph theoretical approach to realize various quantum experiments. Crucially, we may represent quantum optical experiments involving tabletop optical elements in terms of highly interpretable, coloured, weighted multi-graphs. We introduce the formalism behind this approach; then through the digital discovery framework PyTheus, we uncover over 100 different quantum experiments which realizes complex, novel quantum states. Towards enhancing our interpretation of the AI-based framework's solutions, we also leverage eXplainable-AI (XAI) techniques from computer vision to investigate what a trained neural network learns about quantum experiments. Crucially, we find that we are able to conceptualize the learned strategies which the neural network applies to optimize for a target quantum property, and discover how the network conceives of its solution. We conclude by presenting an experimental proposal which yields realizable solutions that, for the first time, solves high-dimensional variants of a quantum retrodiction puzzle known as the Mean King's Problem. We, therefore, present a case study which investigates the potential for new scientific discoveries through a joint collaboration between human and artificial intelligence.

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The trend today is to use many inexpensive sensors instead of a few expensive ones, since the same accuracy can generally be obtained by fusing several dependent measurements. It also follows that the robustness against failing sensors is improved. As a result, the need for high-dimensional regression techniques is increasing. As measurements are dependent, the regressors will be constrained to some manifold. There is then a representation of the regressors, of the same dimension as the manifold, containing all predictive information. Since the manifold is commonly unknown, this representation has to be estimated using data. For this, manifold learning can be utilized. Having found a representation of the manifold constrained regressors, this low-dimensional representation can be used in an ordinary regression algorithm to find a prediction of the output. This has further been developed in the Weight Determination by Manifold Regularization (WDMR) approach. In most regression problems, prior information can improve prediction results. This is also true for high-dimensional regression problems. Research to include physical prior knowledge in high-dimensional regression i.e., gray-box high-dimensional regression, has been rather limited, however. We explore the possibilities to include prior knowledge in high-dimensional manifold constrained regression by the means of regularization. The result will be called gray-box WDMR. In gray-box WDMR we have the possibility to restrict ourselves to predictions which are physically plausible. This is done by incorporating dynamical models for how the regressors evolve on the manifold. / MOVIII

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