Navigation with unmanned aerial vehicles (UAVs) requires good knowledge of the current position and other states. A UAV navigation system often uses GPS and inertial sensors in a state estimation solution. If the GPS signal is lost or corrupted state estimation must still be possible and this is where simultaneous localization and mapping (SLAM) provides a solution. SLAM considers the problem of incrementally building a consistent map of a previously unknown environment and simultaneously localize itself within this map, thus a solution does not require position from the GPS receiver. This thesis presents a visual feature based SLAM solution using a low resolution video camera, a low-cost inertial measurement unit (IMU) and a barometric pressure sensor. State estimation in made with a extended information filter (EIF) where sparseness in the information matrix is enforced with an approximation. An implementation is evaluated on real flight data and compared to a EKF-SLAM solution. Results show that both solutions provide similar estimates but the EIF is over-confident. The sparse structure is exploited, possibly not fully, making the solution nearly linear in time and storage requirements are linear in the number of features which enables evaluation for a longer period of time.

The first part of the dissertation concerns the Ising problem proposed to Ernst Ising by his supervisor Wilhelm Lenz in the early 20s. The Ising model, or perhaps more correctly the Lenz-Ising model, tries to capture the behaviour of phase transitions, i.e. how local rules of engagement can produce large scale behaviour. Two decades later Lars Onsager solved the Ising problem for the quadratic lattice without an outer field. Using his ideas solutions for other lattices in two dimensions have been constructed. We describe a method for calculating the Ising partition function for immense square grids, up to linear order 320 (i.e. 102400 vertices). In three dimensions however only a few results are known. One of the most important unanswered questions is at which temperature the Ising model has its phase transition. In this dissertation it is shown that an upper bound for the critical coupling Kc, the inverse absolute temperature, is 0.29 for the tree dimensional cubic lattice. To be able to get more information one has to use different statistical methods. We describe one sampling method that can use simple state generation like the Metropolis algorithm for large lattices. We also discuss how to reconstruct the entropy from the model, in order to obtain parameters as the free energy. The Ising model gives a partition function associated with all finite graphs. In this dissertation we show that a number of interesting graph invariants can be calculated from the coefficients of the Ising partition function. We also give some interesting observations about the partition function in general and show that there are, for any N, N non-isomorphic graphs with the same Ising partition function. The second part of the dissertation is about matrix operations. We consider the problem of multiplying them when the entries are elements in a finite semiring or in an additively finitely generated semiring. We describe a method that uses O(n3 / log n) arithmetic operations. We also consider the problem of reducing n x n matrices over a finite field of size q using O(n2 / logq n) row operations in the worst case.

No description available.

This dissertation shows that nonnegative matrix factorization (NMF) can be extended to a general and efficient clustering method. Clustering is one of the fundamental tasks in machine learning. It is useful for unsupervised knowledge discovery in a variety of applications such as text mining and genomic analysis. NMF is a dimension reduction method that approximates a nonnegative matrix by the product of two lower rank nonnegative matrices, and has shown great promise as a clustering method when a data set is represented as a nonnegative data matrix. However, challenges in the widespread use of NMF as a clustering method lie in its correctness and efficiency: First, we need to know why and when NMF could detect the true clusters and guarantee to deliver good clustering quality; second, existing algorithms for computing NMF are expensive and often take longer time than other clustering methods. We show that the original NMF can be improved from both aspects in the context of clustering. Our new NMF-based clustering methods can achieve better clustering quality and run orders of magnitude faster than the original NMF and other clustering methods. Like other clustering methods, NMF places an implicit assumption on the cluster structure. Thus, the success of NMF as a clustering method depends on whether the representation of data in a vector space satisfies that assumption. Our approach to extending the original NMF to a general clustering method is to switch from the vector space representation of data points to a graph representation. The new formulation, called Symmetric NMF, takes a pairwise similarity matrix as an input and can be viewed as a graph clustering method. We evaluate this method on document clustering and image segmentation problems and find that it achieves better clustering accuracy. In addition, for the original NMF, it is difficult but important to choose the right number of clusters. We show that the widely-used consensus NMF in genomic analysis for choosing the number of clusters have critical flaws and can produce misleading results. We propose a variation of the prediction strength measure arising from statistical inference to evaluate the stability of clusters and select the right number of clusters. Our measure shows promising performances in artificial simulation experiments. Large-scale applications bring substantial efficiency challenges to existing algorithms for computing NMF. An important example is topic modeling where users want to uncover the major themes in a large text collection. Our strategy of accelerating NMF-based clustering is to design algorithms that better suit the computer architecture as well as exploit the computing power of parallel platforms such as the graphic processing units (GPUs). A key observation is that applying rank-2 NMF that partitions a data set into two clusters in a recursive manner is much faster than applying the original NMF to obtain a flat clustering. We take advantage of a special property of rank-2 NMF and design an algorithm that runs faster than existing algorithms due to continuous memory access. Combined with a criterion to stop the recursion, our hierarchical clustering algorithm runs significantly faster and achieves even better clustering quality than existing methods. Another bottleneck of NMF algorithms, which is also a common bottleneck in many other machine learning applications, is to multiply a large sparse data matrix with a tall-and-skinny dense matrix. We use the GPUs to accelerate this routine for sparse matrices with an irregular sparsity structure. Overall, our algorithm shows significant improvement over popular topic modeling methods such as latent Dirichlet allocation, and runs more than 100 times faster on data sets with millions of documents.

Stowaway/matrix attachment regions (S/MARS) are sequences of DNA that anchor chromatin to the nuclear matrix, function in gene expression, chromatin organization, and conformation. Current identification tools in Eukaryotes rely on a small population of known S/MARs for search criterion. This study presents bioinformatics prediction of S/MARs across various genomes using the program Basic Local Alignment Search Tool (BLAST), providing an opportunity to identify putative S/MARs for further characterization and a novel application of BLAST for S/MAR identification. Two wheat S/MARs were used to identify homologous sequences, within the true grasses, or Gramineae. The evidence suggests that S/MARs are prolific in Gramineae species, specifically in the related subspecies Triticeae. In addition, stowaway-like sequences associated with predicted S/MARs within Gramineae species are present, found to be in association with predicted S/MARs in Gramineae, and proposed to be the product of an unknown duplication mechanism and bear no significant association with S/MARs. / Department of Biology

In Alzheimer’s disease (AD), different types of neurons and different brain areas show differential patterns of vulnerability towards neurofibrillary degeneration, which provides the basis for a highly predictive profile of disease progression throughout the brain that now is widely accepted for neuropathological staging. In previous studies we could demonstrate that in AD cortical and subcortical neurons are constantly less frequently affected by neurofibrillary degeneration if they are enwrapped by a specialized form of the hyaluronan-based extracellular matrix (ECM), the so called ‘perineuronal net’ (PN). PNs are basically composed of large aggregating chondroitin sulphate proteoglycans connected to a hyaluronan backbone, stabilized by link proteins and cross-linked via tenascin-R (TN-R). Under experimental conditions in mice, PN-ensheathed neurons are better protected against iron-induced neurodegeneration than neurons without PN. Still, it remains unclear whether these neuroprotective effects are directly mediated by the PNs or are associated with some other mechanism in these neurons unrelated to PNs. To identify molecular components that essentially mediate the neuroprotective aspect on PN-ensheathed neurons, we comparatively analysed neuronal degeneration induced by a single injection of FeCl3 on four different mice knockout strains, each being deficient for a different component of PNs. Aggrecan, link protein and TN-R were identified to be essential for the neuroprotective properties of PN, whereas the contribution of brevican was negligible. Our findings indicate that the protection of PN-ensheathed neurons is directly mediated by the net structure and that both the high negative charge and the correct interaction of net components are essential for their neuroprotective function.

Integrations over the unitary group are required in many applications including the joint eigenvalue distributions of the Wishart matrices. In this thesis, a universal integration framework is proposed to use the character expansions for any unitary integral with general rectangular complex matrices in the integrand. The proposed method is applied to solve some of the well--known but not solved in general form unitary integrals in their general forms, such as the generalized Harish--Chandra--Itzykson--Zuber integral. These integrals have applications in quantum chromodynamics and color--flavor transformations in physics. The unitary integral results are used to obtain new expressions for the joint eigenvalue distributions of the semi--correlated and full--correlated central Wishart matrices, as well as the i.i.d. and uncorrelated noncentral Wishart matrices, in a unified approach. Compared to the previous expressions in the literature, these new expressions are much easier to compute and also to apply for further analysis. In addition, the joint eigenvalue distribution of the full--correlated case is a new result in random matrix theory. The new distribution results are employed to obtain the individual eigenvalue densities of Wishart matrices, as well as the capacity of multiple--input multiple--output (MIMO) wireless channels. The joint eigenvalue distribution of the i.i.d. case is used to obtain the largest eigenvalue density and the bit error rate (BER) of the optimal beamforming in finite--series expressions. When complete channel state information is not available at the transmitter, a codebook of beamformers is used by the transmitter and the receiver. In this thesis, a codebook design method using the genetic algorithm is proposed, which reduces the design complexity and achieves large minimum--distance codebooks. Exploiting the specific structure of these beamformers, an order and bound algorithm is proposed to reduce the beamformer selection complexity at the receiver side. By employing a geometrical approach, an approximate BER for limited feedback beamforming is derived in finite--series expressions.

Diss. (sammanfattning) Stockholm : Karol. inst., 2004. / Härtill 5 uppsatser.

Diss. (sammanfattning) Stockholm : Karol. inst., 2004. / Härtill 4 uppsatser.

Diss. (sammanfattning) Stockholm : Karolinska institutet, 2005. / Härtill 4 uppsatser.