THE transition to sustainable energy requires cleaner and more efficient ways to consume heat.We are used to our homes and offices being warm, yet behind this expectation lies infrastructure that must continuously balance supply and demand: heat must be produced, transported, and delivered exactly when and where it is needed. District heating networks accomplish this by circulating hot water through underground pipelines, connecting heat sources to thousands of buildings across a city. Operating such a network efficiently is far from trivial. Decisions made now about how much heat to produce, at what temperature, and through which routes have consequences that unfold over hours as hot water slowly travels through kilometers of pipe. Getting these decisions right can mean significant cost savings; getting them wrong leads to wasted energy or discomfort.
This challenge is fundamentally one of planning under complexity. The operator must anticipate future demand, account for heat losses during transport, respect physical limitations of pumps and pipes, and respond to fluctuating energy prices, all while the state of the network is only partially observable through a limited set of sensors. Traditional approaches rely on simple rules and operator experience, which suffice for conventional high-temperature networks but fall short as renewable sources have lower temperatures, requiring more advanced anticipative control strategies.
This thesis develops computational methods that enable district heating networks to be operated efficiently in real time. The underlying physics lead to mathematical optimization problems that are, in their original form, too complex to solve within practical time limits. This thesis introduces techniques that reformulate these problems into more tractable forms, decompose them across time to reduce computational burden, and learn efficient representations from operational data.We also address the question of where to place sensors to best reconstruct the network state, and establish theoretical conditions that guarantee stable closed-loop operation.
These methods are validated on realistic network models and compared against conventional rule-based strategies. The results show that predictive control can meaningfully reduce operating costs while improving constraint satisfaction, that our sensor placement method provides a practical tool for selecting informative measurement locations under tight instrumentation budgets, and that computational decomposition and data-driven surrogate models each bring solve times within real-time limits without sacrificing performance. We further find evidence of inherent stability properties of the closed-loop system, even in the absence of terminal constraints. Together, these findings demonstrate that the fundamental barriers to deploying advanced control in district heating networks can be systematically addressed.

Meditation is a contemplative practice that is believed to entail attentional and emotional regulation. One of the biggest challenges in developing personalized, accessible healthcare options with meditation is finding understandable features that signify whether someone is meditating. Specifically, there is no consensus on a feature resulting from the electroencephalogram (EEG) in the current body of literature on meditation.

In this thesis, I propose a dynamic systems analysis on EEG data to obtain a dynamic feature capable of distinguishing meditation from an eyes-closed resting baseline. I gathered the EEG data at TNO (Dutch Organisation for Applied Scientific Research) from twenty-two participants during a sixteen-minute loving-kindness meditation and two two-minute baselines. The proposed methodology characterizes temporal and spatial characteristics of the EEG simultaneously by approximating the EEG dynamics with a linear model on short time windows. I assess changes among three features: the frequency and magnitude of the oscillatory dynamics and the corresponding active electrodes.

The analysis can identify changes in EEG dynamics for each individual. Across all participants, regions associated with vision and language processing were active throughout the experiment. Notably, attention-related regions were more involved during meditation than rest. Moreover, the results show a shift in active regions throughout the meditation and the baselines for several participants.

Moreover, the thesis investigates the sensitivity of the analytical approach to changes in the electrode subset used for the analysis. For each participant, I constructed a subset of electrodes that were most involved in the changing EEG dynamics. The personalized subset was most sensitive to changes between meditation and rest, compared to other subsets based on commercial wearable EEG headsets. Finally, I compare the findings of the dynamic systems approach to a conventional analytical approach, and the participants’ emotional ratings inquired in subjective questionnaires. Unfortunately, from the current data, there appears to be no relationship between the proposed features and the conventional measures or the subjective questionnaires.

In this thesis, I introduce a novel model identification approach to time series forecasting. For linear stationary processes, such as AR processes, the direction of time is independent of the model parameters. By combining theoretical principles of time-reversibility in time series with conventional modeling approaches such as information criteria, I design a criterion that employs the backwards prediction (backcast) as a proxy for the forecast. Hereby, I aim to adopt a finite sample, data-driven approach to model selection. The novel criterion is named the \textit{backwards validated information criterion (BVIC)}. The \acs{BVIC} quantifies forecasting performance of models by trading off a measure of \mbox{goodness-of-fit} and a models ability to predict backwards. I test the performance of the BVIC by conducting experiments on synthetic and real data. In each experiment, the BVIC is examined in contrast to conventionally employed criteria.

Experimental results suggest that the BVIC has comparable performance to conventional information criteria. Specifically, in most of the experiments performed, I did not find statistically significant differences between the forecast error of the BVIC under certain parameterizations and that of the different information criteria. Nonetheless, it is worth emphasizing that the BVIC guarantees are established by design where the model order penalization term depends on strong mathematical properties of time-reversibility and a finite data assessment. In particular, the penalization term is replaced by a weighted trade-off between functional dimensions pertaining to forecasting.


That said, I observed that the BVIC recovered more accurately the real order of the underlying process than the other criteria, which rely on a static penalization of the model order. Lastly, leveraging the latter property, I perform the assessment of the order model (or, memory) of time series pertaining to epileptic seizures recorded using electrocorticographic data. The results provide converging evidence that the order of the model increases during the epileptic events.

Resting-state functional magnetic resonance imaging (rs-fMRI) is one of the promising non-invasive technology that helps in the detection of neurodegenerative and neurological disorders, localisation of the different areas of the brain and understanding the connectivity between them. It involves the acquisition of time series of MR images while the brain is at "resting-state" and serves as a biomarker for various neurological conditions. The acquired resting-state blood-oxygen-level-dependent (BOLD) data, however, can be corrupted with various artefacts (head movements, physiological movements like breathing etc.). Several preprocessing pipelines have been developed to counter the effect of these known artefacts. However, there might be some artefacts that could not have been attenuated from the signal and might lead to incorrect assessment. Therefore, the thesis proposes model-based filtering of the minimally preprocessed (free from known artefacts) resting-state BOLD signal. It was observed that these signals have long memory dependencies. Hence, the usage of autoregressive fractional integrative process filters is proposed for this purpose.
Furthermore, the utility of the approach is demonstrated by removing the effect of white noise from a synthetic signal with statistical properties similar to the resting-state BOLD signal. Afterwards, the proposed method is implemented on the minimally preprocessed resting-state BOLD data of 98 subjects from the Human Connectome Project. The results suggest that the proposed filter, in contrast to the low-pass filter, attenuates the higher frequencies but do not eliminate them. Additionally, four different evaluation measures (power spectrum, functional connectivity using Pearson's correlation and coherence, and eigenmode analysis) were considered. The results provide evidence that the proposed method can be used as an additional step in the already existing preprocessing pipeline to mitigate some artefacts that could not have been filtered out. Besides, the results also provide evidence that the proposed scheme is suitable to capture the dynamics of resting-state BOLD signals.

General anesthesia (GA) is an important medical procedure that induces unconsciousness to patients during surgery. Consciousness is a salient feature of the brain, whose neurophysiological features are difficult to be distinguished from unconsciousness. Though it can be defined as an event arising due to interactions in the nervous system, it entirely is not a reliable mechanism. Thus, tracking changes in the brain waves caused by GA is a challenging problem in neuroscience. The exact mechanism to quantify the state of the brain and to distinguish between conscious and unconscious brain is still difficult. Specific features to characterize the state of the brain from the patterns of the brain signal is challenging. Present-day depth of anesthesia monitors index values does not quantify the state of the brain.

An alternative approach is to use dynamical systems theory to assess the underlying dynamics of the brain with imaging technology (e.g., electroencephalographic and electrocorticographic data). Previous results from the literature suggest that stability can play a role in the characterization of unconsciousness. This thesis proposes a detailed study that focus on dynamical systems properties that go beyond stability. In particular, the proposed methodology aims to assess which regions of the brain intervene in the process of consciousness and unconsciousness, as well as quantify how often they interact with each other. Specifically, the approach seeks to leverage the eigenstructure of the underlying approximation of the neural activity captured from intracranial electrocorticographic data.

Our results show that it is possible to differentiate between anesthetic stages of the brain using eigendecomposition. This was possible through a framework that provides a regularised way to sparsify the state estimates of electrocorticographic (ECoG) signal to get a model for analysis of changes in the brain waves affected by GA. Later to look at the eigenvalues and eigenvectors, which gives the frequency of oscillation and direction between different regions of the brain, respectively. It was also observed that the pattern in the evolution of eigenvalues during different anesthetic stages could be able to interpret if the subject was under anesthesia or not.