Cellular automata (CA) have been widely used as idealized models of spatially-extended dynamical systems and as models of massively parallel distributed computation devices. Despite their wide range of applications and the fact that CA are capable of universal computation (under particular constraints), the full potential of these models is unrealized to-date. This is for two reasons: (1) the absence of a programming paradigm to control these models to solve a given problem and (2) the lack of understanding of how these models compute a given task. This work addresses the notion of computation in two-dimensional cellular automata. Solutions using a decentralized parallel model of computation require information processing on a global level. CA have been used to solve the so-called density (or majority) classification task that requires a system-wide coordination of cells. To better understand and challenge the ability of CA to solve problems, I define, solve, and analyze novel tasks that require solutions with global information processing mechanisms. The ability of CA to perform parallel, collective computation is attributed to the complex pattern-forming system behavior. I further develop the computational mechanics framework to study the mechanism of collective computation in two-dimensional cellular automata. I define several approaches to automatically identify the spatiotemporal structures with information content. Finally, I demonstrate why an accurate model of information processing in two-dimensional cellular automata cannot be constructed from the space-time behavior of these structures.

Filtering or estimation is of great importance to virtually all disciplines of engineering and science that need inference, learning, information fusion, and knowledge discovery of dynamical systems. The filtering problem is to recursively determine the states and/or parameters of a dynamical system from a sequence of noisy measurements made on the system. The theory and practice of optimal estimation of linear Gaussian dynamical systems have been well established and successful, but optimal estimation of nonlinear and non-Gaussian dynamical systems is much more challenging and in general requires solving partial differential equations and intractable high-dimensional integrations. Hence, Gaussian approximation filters are widely used. In this dissertation, three innovative point-based Gaussian approximation filters including sparse Gauss-Hermite quadrature filter, sparse-grid quadrature filter, and the anisotropic sparse-grid quadrature filter are proposed. The relationship between the proposed filters and conventional Gaussian approximation filters is analyzed. In particular, it is proven that the popular unscented Kalman filter and the cubature Kalman filter are subset of the proposed sparse-grid filters. The sparse-grid filters are employed in three aerospace applications including spacecraft attitude estimation, orbit determination, and relative navigation. The results show that the proposed filters can achieve better estimation accuracy than the conventional Gaussian approximation filters, such as the extended Kalman filter, the cubature Kalman filter, the unscented Kalman filter, and is computationally more efficient than the Gauss-Hermite quadrature filter.

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Tractography is widely used in the brain connectivity study from diffusion magnetic resonance imaging data. However, lack of ground truth and plenty of anatomically implausible streamlines in the tractograms have caused challenges and concerns in the use of tractograms such as brain connectivity study. Tractogram filtering methods have been developed to remove the faulty connections. In this study, we focus on one of these filtering methods, Convex Optimization Modeling for Microstructure Informed Tractography (COMMIT), which tries to find a set of streamlines that best reconstruct the diffusion magnetic resonance imaging data with global optimization approach. There are biases with this method when assessing individual streamlines. So a method named randomized COMMIT(rCOMMIT) is proposed to obtain multiple assessments for each streamline. The acceptance rate from this method is introduced to the streamlines and divides them into three groups, which are regarded as pseudo ground truth from rCOMMIT. Therefore, the neural networks are able to train on the pseudo ground truth on classification tasks. The trained classifiers distinguish the obtained groups of plausible and implausible streamlines with accuracy around 77%. Following the same methodology, the results from rCOMMIT and randomized SIFT are compared. The intersections between two methods are analyzed with neural networks as well, which achieve accuracy around 87% in binary task between plausible and implausible streamlines.

In the study, two methods for recommending application software were implemented and evaluated based on their ability to recommend alternative applications with related functionality to the one that a user is currently browsing. One method was based on Term Frequency–Inverse Document Frequency (TF-IDF) and the other was based on Latent Semantic Indexing (LSI). The dataset used was a set of 2501 articles from Wikipedia, each describing a distinct application. Two experiments were performed to evaluate the methods. The first experiment consisted of measuring to what extent the recommendations for an application belong to the same software category, and the second was a set of structured interviews in which recommendations for a subset of the applications in the dataset were evaluated more in-depth. The results from the two experiments showed only a small difference between the methods, with a slight advantage to LSI for smaller sets of recommendations retrieved, and an advantage for TF-IDF for larger sets of recommendations retrieved. The interviews indicated that the recommendations from when LSI was used to a higher extent had a similar functionality as the evaluated applications. The recommendations from when TF-IDF was used had a higher fraction of applications with functionality that complemented or enhanced the functionality of the evaluated applications. / I studien implementerades och utvärderades två alternativa implementationer av ett rekommendationssystem för applikationsprogramvara. Implementationerna utvärderades baserat på deras förmåga att föreslå alternativa applikationer med relaterad funktionalitet till den applikation som användaren av ett system besöker eller visar. Den ena implementationen baserades på Term Frequency-Inverse Document Frequency (TF-IDF) och den andra på Latent Semantic Indexing (LSI). Det data som användes i studien bestod av 2501 artiklar från engelska Wikipedia, där varje artikel bestod av en beskrivning av en applikation. Två experiment utfördes för att utvärdera de båda metoderna. Det första experimentet bestod av att mäta till vilken grad de rekommenderade applikationerna tillhörde samma mjukvarukategori som den applikation de rekommenderats som alternativ till. Det andra experimentet bestod av ett antal strukturerade intervjuer, där rekommendationerna för en delmängd av applikationerna utvärderades mer djupgående. Resultaten från experimenten visade endast en liten skillnad mellan de båda metoderna, med en liten fördel till LSI när färre rekommendationer hämtades, och en liten fördel för TF-IDF när fler rekommendationer hämtades. Intervjuerna visade att rekommendationerna från den LSI-baserade implementationen till en högre grad hade liknande funktionalitet som de utvärderade applikationerna, och att rekommendationerna från när TF-IDF användes till en högre grad hade funktionalitet som kompletterade eller förbättrade de utvärderade applikationerna.

Brain-Computer Interface (BCI) offers the opportunity to paralyzed patients to control their movements without any neuromuscular activity. Signal processing of neuronal activity enables to decode movement intentions. Ability for patient to control an effector is closely linked to this decoding performance. In this study, I tackle a recent way to decode neuronal activity: Deep learning. The study is based on public data extracted by Schalk et al. for BCI Competition IV. Electrocorticogram (ECoG) data from three epileptic patients were recorded. During the experiment setup, the team asked subjects to move their fingers and recorded finger movements thanks to a data glove. An artificial neural network (ANN) was built based on a common BCI feature extraction pipeline made of successive convolutional layers. This network firstly mimics a spatial filtering with a spatial reduction of sources. Then, it realizes a time-frequency analysis and performs a log power extraction of the band-pass filtered signals. The first investigation was on the optimization of the network. Then, the same architecture was used on each subject and the decoding performances were computed for a 6-class classification. I especially investigated the spatial and temporal filtering. Finally, a preliminary study was conducted on prediction of finger movement. This study demonstrated that deep learning could be an effective way to decode brain signal. For 6-class classification, results stressed similar performances as traditional decoding algorithm. As spatial or temporal weights after training are slightly described in the literature, we especially worked on interpretation of weights after training. The spatial weight study demonstrated that the network is able to select specific ECoG channels notified in the literature as the most informative. Moreover, the network is able to converge to the same spatial solution, independently to the initialization. Finally, a preliminary study was conducted on prediction of movement position and gives encouraging results.

High-pass filtering has been shown to be a promising method for edge detection in optical scanning holography. By using a circular function as a pupil for the system, the radius of the circle can be varied to block out different ranges of frequencies. Implementing this system in simulation yields an interesting result, however. As the radius increases, a singular edge can split off into two edges instead. To understand the specific conditions under which this split occurs, Airy pattern filtering and single-sided filtering were implemented to analyze the results from the original high-pass simulation. These methods were tested with different input objects to assess any common patterns. Ultimately, no definitive answer was found, as Airy pattern filtering resulted in inconsistent results across different input objects, and single-sided filtering does not completely isolate the edge. Nonetheless, the documented results may aid a future understanding of this phenomenon. / Master of Science / Holograms are three-dimensional recordings of an object, reminiscent of how a photograph records a two-dimensional image of an object. Detecting edges in images and the reconstructed images from holograms can help us identify objects within the recorded image or hologram. In computer vision, common edge detection techniques involve analyzing the image's spatial frequency, or changes in relative intensity over space. One such technique is high-pass filtering, in which lower spatial frequencies are blocked out. High-pass filtering can also be applied to holographic imaging systems. However, when applying high-pass filtering to a holographic system, detected edges can split into two as higher frequencies are filtered out. This thesis examines the conditions for why this split-edge phenomenon occurs by modifying the original recorded object and the filtering mechanism, then analyzing the resultant holograms. While the results did not give a conclusive answer, they have been documented for the purpose of further research.

No / Radio Frequency Identification (RFID) technology has been widely applied in many scenarios such as inventory control, supply chain management due to its superior properties including fast identification and relatively long interrogating range over barcode systems. It is critical to efficiently identify the unknown tags because these tags can appear when new tagged objects are moved in or wrongly placed. The state-of-the-art Basic Unknown tag Identification Protocol-with Collision-Fresh slot paring (BUIP-CF) protocol can first deactivate all the known tags and then collect all the unknown tags. However, BUIP-CF protocol investigates an ALOHA-like technique and causes too many tag responses, which results in low efficiency. This paper proposes a Fast Unknown tag Identification (FUI) protocol which investigates an indicator vector to label the unknown tags with a given accuracy and removes the time-consuming tag responses in the deactivation phase. FUI also adopts the classical Enhanced Dynamic Framed Slotted ALOHA (EDFSA) protocol to collect the labeled unknown tags. We then investigate the optimal parameter settings to maximize the performance of the proposed FUI protocol. Extensive simulation experiments are conducted to evaluate the performance of the proposed FUI protocol and the experimental results show that it considerably outperforms the state-of-the-art protocol.

<p>Multi-Target Tracking (MTT), where the number of targets as well as their states are time-varying, concerns with the estimation of both the number of targets and the individual states from noisy sensor measurements, whose origins are unknown. Filtering typically produces the best estimates of the target state based on all measurements up to current estimation time. Smoothing or retrodiction, which uses measurements beyond the current estimation time, provides better estimation of target states. This thesis proposes smoothing methods for various estimation methods that produce delayer, but better, estimates of the target states.</p> <p>First, we propose a novel smoothing method for the Probability Hypothesis Density (PHD) estimator. The PHD filer, which propagates the first order statistical moment of the multitarget state density, a computationally efficient MTT algorithm. By evaluating the PHD, the number of targets as well as their individual states can be extracted. Recent Sequential Monte Carlo (SMC) implementations of the PHD filter have paved the way to its application to realistic nonlinear non-Gaussian problems. The proposed PHD smoothing method involves forward multitarget filtering using the standard PHD filter recursion followed by backward smoothing recursion using a novel recursive formula.</p> <p>Second, we propose a Multiple Model PH (MMPHD) smoothing method for tracking of maneuvering targets. Multiple model approaches have been shown to be effective for tracking maneuvering targets. MMPHD filter propagates mode-conditioned PHD recursively. The proposed backward MMPHD smoothing algorithm involves the estimation of a continuous state for target dynamic as well as a discrete state vector for the mode of target dynamics.</p> <p>Third, we present a smoothing method for the Gaussian Mixture PHD (GMPHD) state estimator using multiple sensors. Under linear Gaussian assumptions, the PHD filter can be implemented using a closed-form recursion, where the PHD is represented by a mixture of Gaussian functions. This can be extended to nonlinear systems by using the Extended Kalman Filter (EKF) or the Unscented Kalman Filter (UKF). In the case of multisenor systems, a sequential update of the PHD has been suggested in literature. However, this sequential update is susceptible to imperfections in the last sensor. In this thesis, a parallel update for GMPHD filter is proposed. The resulting filter outputs are further improved using a novel closed-form backward smoothing recursion.</p> <p>Finally, we propose a novel smoothing method for Kalman based Interacting Multiple Model (IMM) estimator for tracking agile targets. The new method involves forwarding filtering followed by backward smoothing while maintaining the fundamental spirit of the IMM. The forward filtering is performed using the standard IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion. This backward recursion mimics the IMM estimator in the backward direction, where each mode conditioned smoother uses standard Kalman smoothing recursion.</p> / Thesis / Doctor of Philosophy (PhD)

A new method of realizing linear, time-invariant digital filters is developed and demonstrated. The result is based on the convolution integral. It is assumed that the specifications of the filter are known and from these, an appropriate analog filter is chosen. The properties of this filter are then retained by digital filter after transformation. The behaviour of lowpass, highpass bandpass and bandstop digital filters is investigated in both the frequency and time domains, for both cascade and parallel structure is superior for lowpass and bandpass digital filters, and that the cascade structure is superior for high pass and bandstop digital filters. / Thesis / Master of Engineering (ME)