Using sensors to observe real-world systems is important in many applications. A typical use case is target tracking, where sensor measurements are used to compute estimates of targets. Two of the main purposes of the estimates are to enhance situational awareness and facilitate decision-making. Hence, the estimation quality is crucial. By utilizing multiple sensors, the estimation quality can be further improved. Here, the focus is on target tracking in decentralized sensor networks, where multiple agents estimate a common set of targets. In a decentralized context, measurements undergo local preprocessing at the agent level, resulting in local estimates. These estimates are subsequently shared among the agents for estimate fusion. Sharing information leads to correlations between estimates, which in decentralized sensor networks are often unknown. In addition, there are situations where the communication capacity is constrained, such that the shared information needs to be reduced. This thesis addresses two aspects of decentralized target tracking: (i) fusion of estimates with unknown correlations; and (ii) handling of constrained communication resources. 

Decentralized sensor networks have unknown correlations because it is typically impossible to keep track of dependencies between estimates. A common approach in this case is to use conservative estimators, which can ensure that the true uncertainty of an estimate is not underestimated. This class of estimators is pursued here. A significant part of the thesis is dedicated to the widely-used conservative method known as covariance intersection (CI), while also describing and deriving alternative methods for CI. One major result related to aspect (i) is the conservative linear unbiased estimator (CLUE), which is proposed as a general framework for optimal conservative estimation. It is shown that several existing methods, including CI, are optimal CLUEs under different conditions. 

A decentralized sensor network allows for less data to be communicated compared to its centralized counterpart. Yet, there are still situations where the communication load needs to be further reduced. The communication load is mostly driven by the covariance matrices since, in this scope, estimates and covariance matrices are shared. One way to reduce the communication load is to only exchange parts of the covariance matrix. To this end, several methods are proposed that preserve conservativeness. Significant results related to aspect (ii) include several algorithms for transforming exchanged estimates into a lower-dimensional subspace. Each algorithm corresponds to a certain estimation method, and for some of the algorithms, optimality is guaranteed. Moreover, a framework is developed to enable the use of the proposed dimension-reduction techniques when only local information is available at an agent. Finally, an optimization strategy is proposed to compute dimension-reduced estimates while maintaining data association quality. 

The protection of confidential data is a fundamental need in the society in which we live. This task becomes more relevant when observing that every day, data traffic increases exponentially, as well as the number of attacks on the telecommunication infra-structure. From the natural sciences, it has been strongly argued that quantum communication has great potential to solve this problem, to such an extent that various governmental and industrial entities believe the protection provided by quantum communications will be an important layer in the field of information security in the next decades. However, integrating quantum technologies both in current optical networks and in industrial systems is not a trivial task, taking into account that a large part of current quantum optical systems are based on bulk optical devices, which could become an important limitation. Throughout this thesis we present an all-in-fiber optical platform that allows a wide range of tasks that aim to take a step forward in terms of generation and detection of photonic states. Among the main features, the generation and detection of photonic quantum states carrying orbital angular momentum stand out.   

The platform can also be configured for the generation of random numbers from quantum mechanical measurements, a central aspect in future information tasks.  

Our scheme is based on the use of new space-division-multiplexing (SDM) technologies such as few-mode-fibers and photonic lanterns. Furthermore, our platform can also be scaled to high dimensions, it operates in 1550 nm (telecommunications band) and all the components used for its implementation are commercially available. The results presented in this thesis can be a solid alternative to guarantee the compatibility of new SDM technologies in emerging experiments on optical networks and open up new possibilities for quantum communication. 

The trend of automation in industry, and in the society in general, is something that probably all of us have noticed. The mining industry is no exception to this trend, and there exists a vision of having completely automated mines with all processes monitored and controlled through a higher level optimization goal. For this vision, access to a reliable positioning system has been identified a prerequisite. Underground mines posses extraordinary premises for localization, due to the harsh, unstructured and ever changing environment, where existing localization solutions struggle with accuracy and reliability over time. 

This thesis addresses the problem of achieving accurate, robust and consistent position estimates for long-term autonomy of vehicles operating in an underground mining environment. The focus is on onboard positioning solutions utilizing sensor fusion within the probabilistic filtering framework, with extra emphasis on the characteristics of lidar data. Contributions are in the areas of improved state estimation algorithms, more efficient lidar data processing and development of models for changing environments. The problem descriptions and ideas in this thesis are sprung from underground localization issues, but many of the resulting solutions and methods are valid beyond this application. 

In this thesis, internal localization algorithms and data processing techniques are analyzed in detail. The effects of tuning the parameters in an unscented Kalman filter are examined and guidelines for choosing suitable values are suggested. Proper parameter values are shown to substantially improve the position estimates for the underground application. Robust and efficient processing of lidar data is explored both through analysis of the information contribution of individual laser rays, and through preprocessing in terms of feature extraction. Methods suitable for available hardware are suggested, and it is shown how it is possible to maintain consistency in the state estimates with less computations. 

Changes in the environment can be devastating for a localization system when characteristics of the observations no longer matches the provided map. One way to manage this is to extend the localization problem to simultaneous localization and mapping (slam). In its standard formulation, slam assumes a truly static surrounding. In this thesis a feature based multi-hypothesis map representation is developed that allows encoding of changes in the environment. The representation is verified to perform well for localization in scenarios where landmarks can attain one of many possible positions. Automatic creation of such maps are suggested with methods completely integrated with the slam framework. This results in a multi-hypothesis slam concept that can discover and adapt to changes in the operation area while at the same time producing consistent state estimates. 

This thesis provides general insights in lidar data processing and state estimation in changing environments. For the underground mine application specifically, different methods presented in this thesis target different aspects of the higher goal of achieving robust and accurate position estimates. Together they present a collective view of how to design localization systems that produce reliable estimates for underground mining environments. 

A mobile robot, instructed by a human operator, acts in an environment with many other objects. However, for an autonomous robot, human instructions should be minimal and only high-level instructions, such as the ultimate task or destination. In order to increase the level of autonomy, it has become a foremost objective to mimic human vision using neural networks that take a stream of images as input and learn a specific computer vision task from large amounts of data. In this thesis, we explore several different models for surround sensing, each of which contributes to a higher understanding of the environment being possible. 

As its first contribution, this thesis presents an object tracking method for video sequences, which is a crucial component in a perception system. This method predicts a fine-grained mask to separate the pixels corresponding to the target from those corresponding to the background. Rather than tracking location and size, the method tracks the initial pixels assigned to the target in this so-called video object segmentation. For subsequent time steps, the goal is to learn how the target looks using features from a neural network. We named our method A-GAME, based on the generative modeling of deep feature space, separating target and background appearances. 

In the second contribution of this thesis, we detect, track, and segment all objects from a set of predefined object classes. This information is how the robot increases its capabilities to perceive the surroundings. We experiment with a graph neural network to weigh all new detections and existing tracks. This model outperforms prior works by separating visually, and semantically similar objects frame by frame. 

The third contribution investigates one limitation of anchor-based detectors, which classify pre-defined bounding boxes as either negative or positive and thus provide a limited set of handled object shapes. One idea is to learn an alternative instance representation. We experiment with a neural network that predicts the distance to the nearest object contour in different directions from each pixel. The network then computes an approximated signed distance function containing the respective instance information. 

Last, this thesis studies a concept within model validation. We observed that overfitting could increase performance on benchmarks. However, this opportunity is insipid for sensing systems in practice since measurements, such as length or angles, are quantities that explain the environment. The fourth contribution of this thesis is an extended validation technique for camera calibration. This technique uses a statistical model for each error difference between an observed value and a corresponding prediction of the projective model. We compute a test over the differences and detect if the projective model is incorrect. 

One of the scopes of Systems Biology is to propose mathematical models that best capture the dynamic behavior of intra-cellular processes. In this regard, the last two decades have brought up a shift in the field, with technological advances now allowing researchers to access a wide range of high-throughput technologies at an affordable cost. These techniques allow to simultaneously interrogate thousands of variables, such as genome-wide transcriptomics and proteomics. However, parallel to these technological advances, there is a growing need for mathematical models that are suited to integrate measurements obtained from different cellular processes.

In this thesis we aim to model combinations of three commonly used high-throughput data: epigenetic (namely ATAC-seq and DNA methylation), transcriptomic (RNA-seq) and proteomic data (MASS-spectrometry). In the first work we analyze paired ATAC-seq and RNA-seq data to integrate measurements of (i) chromatin openness, (ii) transcription factors (TFs) availability and (iii) gene expression. To model these data, we use elementary causal motifs, a class of mathematical models which is suited to represent causal interactions between three nodes. Indeed, our analysis shows that the elementary causal motifs in the data are enriched for biologically relevant TF-gene interactions. Moreover, a significant overlap is observed between the causal motifs identified in datasets representing similar cell stimuli, suggesting that causal motifs represent a robust biological signal.

This work is then extended to include another class of high-throughput data: MASS-spectrometry. More precisely, we propose a framework to model the flow of events that goes from chromatin remodeling to splice variants expression, and from splice variants to protein synthesis. As the underlying graph becomes more complex than the previous case, a more general mathematical framework is considered: Bayesian networks. Interestingly, this work shows that most putative associations between chromatin regions, splice variants and proteins that have been gathered by scientific community so far, are supported by the data. Moreover, similarly to the previous work, the causal interactions identified in the data highlight relevant biological features; more precisely, causal chains between chromatin regions, splice variants and proteins are enriched for splice variants that have a major role in protein synthesis.

From a technical point of view, causal motifs are characterized by a property known as conditional independence, which can be used to identify causal interactions in the data. However, particularly when the data available is limited, it is challenging to assess conditional independencies in the data. It is therefore of interest to investigate the existence of properties that allow us to predict conditional independence. In particular, in our work we propose two properties: structural balance and inverse balance, which are closely connected to what is known in the literature as positive association and multivariate total positivity of order 2 (MTP₂), respectively. Our analysis shows that both heuristics are useful in predicting conditional independence, both from a theoretical perspective and in experimental data.

Lastly, a network-based approach is used to integrate DNA methylation and RNA-seq in a case-control study centered around multiple sclerosis, in order to identify common regulatory patterns in DNA methylation and gene expression during the course of pregnancy. The strategy is based on the rationale that proteins that are interconnected in the protein-protein network are more likely to be involved in similar cellular functions. Indeed, the analysis highlights that similar pathways are altered at epigenetic and transcriptomic level, leading to a set of genes that are likely involved in the modification of the disease symptoms that is observed during pregnancy.