Earthquake swarms occur frequently in West Bohemia, Central Europe. Their occurrence is correlated with and propably triggered by fluids that escape on the earth's surface near the epicentres. These fluids raise up periodically from a seemingbly deep-seated source in the upper mantle. Moment tensors for swarm events in 1997 indicate tensile faulting. However, they were determined under assumption of seismic isotropy although anisotropy can be observed. Anisotropy may obscure moment tensors and their interpretation. In 2000, more than 10,000 swarm earthquakes occurred near Novy Kostel, West Bohemia. Event triggering by fluid injection is likely. Activity lasted from 28/08 until 31/12/00 (9 phases) with maximum ML=3.2. High quality P-wave seismograms were used to retrieve the source mechanisms for 112 events between 28/08/00 and 30/10/00 using > 20 stations. We determine the source geometry using a new algorithm and different velocity models including anisotropy. From inversions of P waves we observe ML<3.2, strike-slip events on steep N-S oriented faults with additional normal or reverse components. Tensile components seem to be evident for more than 60% of the processed swarm events in West Bohemia during the phases 1-7. Being most significant at great depths and at phases 1-4 during the swarm they are time and location dependent. Although tensile components are reduced when anisotropy is assumed they persist and seem to be important. They can be explained by pore-pressure changes due to the injection of fluids that raise up. Our findings agree with other observations e.g. correlation of fluid transport and seismicity, variations in b-value, forcing rate, and in pore pressure diffusion. Tests of our results show their significance.

The complex system of strike-slip and thrust faults in the Alborz Mountains, Northern Iran, are not well understood yet. Mainly structural and geomorphic data are available so far. As a more extensive base for seismotectonic studies and seismic hazard analysis we plan to do a comprehensive seismic moment tensor study also from smaller magnitudes (M < 4.5) by developing a new algorithm. Here, we present first preliminary results.

Functional brain images are extraordinarily rich data sets that reveal distributed brain networks engaged in a wide variety of cognitive operations. It is a substantial challenge both to create models of cognition that mimic behavior and underlying cognitive processes and to choose a suitable analytic method to identify underlying brain networks. Most of the contemporary techniques used in analyses of functional neuroimaging data are based on univariate approaches in which single image elements (i.e. voxels) are considered to be computationally independent measures. Beyond univariate methods (e.g. statistical parametric mapping), multivariate approaches, which identify a network across all regions of the brain rather than a tessellation of regions, are potentially well suited for analyses of brain imaging data. A multivariate method (e.g. partial least squares) is a computational strategy that determines time-varying distributed patterns of the brain (as a function of a cognitive task). Compared to its univariate counterparts, a multivariate approach provides greater levels of sensitivity and reflects cooperative interactions among brain regions. Thus, by considering information across more than one measuring point, additional information on brain function can be revealed. Similarly, by considering information across more than one measuring technique, the nature of underlying cognitive processes become well-understood. Cognitive processes have been investigated in conjunction with multiple neuroimaging modalities (e.g. fMRI, sMRI, EEG, DTI), whereas the typical method has been to analyze each modality separately. Accordingly, little work has been carried out to examine the relation between different modalities. Indeed, due to the interconnected nature of brain processing, it is plausible that changes in one modality locally or distally modulate changes in another modality. This thesis focuses on multivariate and multimodal methods of image analysis applied to various cognitive questions. These methods are used in order to extract features that are inaccessible using univariate / unimodal analytic approaches. To this end, I implemented multivariate partial least squares analysis in study I and II in order to identify neural commonalities and differences between the available and accessible information in memory (study I), and also between episodic encoding and episodic retrieval (study II). Study I provided evidence of a qualitative differences between availability and accessibility signals in memory by linking memory access to modality-independent brain regions, and availability in memory to elevated activity in modality-specific brain regions. Study II provided evidence in support of general and specific memory operations during encoding and retrieval by linking general processes to the joint demands on attentional, executive, and strategic processing, and a process-specific network to core episodic memory function. In study II, III, and IV, I explored whether the age-related changes/differences in one modality were driven by age-related changes/differences in another modality. To this end, study II investigated whether age-related functional differences in hippocampus during an episodic memory task could be accounted for by age-related structural differences. I found that age-related local structural deterioration could partially but not entirely account for age-related diminished hippocampal activation. In study III, I sought to explore whether age-related changes in the prefrontal and occipital cortex during a semantic memory task were driven by local and/or distal gray matter loss. I found that age-related diminished prefrontal activation was driven, at least in part, by local gray matter atrophy, whereas the age-related decline in occipital cortex was accounted for by distal gray matter atrophy. Finally, in study IV, I investigated whether white matter (WM) microstructural differences mediated age-related decline in different cognitive domains. The findings implicated WM as one source of age-related decline on tasks measuring processing speed, but they did not support the view that age-related differences in episodic memory, visuospatial ability, or fluency were strongly driven by age-related differences in white-matter pathways. Taken together, the architecture of different aspects of episodic memory (e.g. encoding vs. retrieval; availability vs. accessibility) was characterized using a multivariate partial least squares. This finding highlights usefulness of multivariate techniques in guiding cognitive theories of episodic memory. Additionally, competing theories of cognitive aging were investigated by multimodal integration of age-related changes in brain structure, function, and behavior. The structure-function relationships were specific to brain regions and cognitive domains. Finally, we urged that contemporary theories on cognitive aging need to be extended to longitudinal measures to be further validated.

Conformal field theories (CFT) constitute an interesting class of twodimensionalquantum field theories, with applications in string theoryas well as condensed matter physics. The symmetries of a CFT can beencoded in the mathematical structure of a conformal vertex algebra.The rational CFT’s are distinguished by the property that the categoryof representations of the vertex algebra is a modular tensor category.The solution of a rational CFT can be split off into two separate tasks, apurely complex analytic and a purely algebraic part. The TFT-construction gives a solution to the second part of the problem.This construction gets its name from one of the crucial ingredients,a three-dimensional topological field theory (TFT). The correlators obtainedby the TFT-construction satisfy all consistency conditions of thetheory. Among them are the factorization constraints, whose implicationsfor boundary conditions are the main topic of this thesis. The main result reviewed in this thesis is that the factorization constraintsgive rise to a semisimple commutative associative complex algebrawhose irreducible representations are the so-called reflection coefficients.The reflection coefficients capture essential information aboutboundary conditions, such as ground-state degeneracies and Ramond-Ramond charges of string compactifications. We also show that the annuluspartition function can be derived fromthis classifying algebra andits representation theory.

Neuroimaging and neurophysiology techniques were used to study some aspects of cortical sensory and motor system reorganisation in patients in the chronic phase after stroke. Using Diffusion Tensor Imaging, we found that the degree of white matter integrity of the corticofugal tracts (CFT) was positively related to grip strength. Structural changes of the CFT were also associated with functional changes in the corticospinal pathways, measured using Transcranial Magnetic Stimulation. This suggests that structural and functional integrity of the CFT is essential for upper limb function after stroke. Using functional magnetic resonance imaging (fMRI), to measure brain activity during slow and fast passive hand movements, we found that velocity-dependent brain activity correlated positively with neural contribution to passive movement resistance in the hand in ipsilateral primary sensory (S1) and motor (M1) cortex in both patients and controls. This suggests a cortical involvement in the hyperactive reflex response of flexor muscles upon fast passive stretch. Effects of a four week passive-active movement training programme were evaluated in chronic stroke patients. The group improved in range of motion and upper limb function after the training. The patients also reported improvements in a variety of daily tasks requiring the use of the affected upper limb. Finally, we used fMRI to explore if brain activity during passive hand movement is related to time after stroke, and if such activity can be affected with intense training. In patients, reduced activity over time was found in supplementary motor area (SMA), contralateral M1 and prefrontal and parietal association areas along with ipsilateral cerebellum. After training, brain activity increased in SMA, ipsilateral S1 and intraparietal sulcus, and contralateral cerebellum in parallel with functional improvements of the upper limb. The findings suggest a use-dependent modification of cortical activation patterns in the affected hand after stroke.

This thesis consists of a summary and three papers, concerning some aspects of representation theory for complex finite dimensional semi-simple Lie algebras with focus on the BGG-category O. Paper I is motivated by the many useful properties of functors on category O given by tensoring with finite dimensional modules, such as projective functors and translation functors. We study properties of functors on O given by tensoring with arbitrary (possibly infinite dimensional) modules. Such functors give rise to a faithful action of O on itself via exact functors which preserve tilting modules, via right exact functors which preserve projective modules, and via left exact functors which preserve injective modules. Papers II and III both deal with Kostant's problem. In Paper II we establish an effective criterion equivalent to the answer to Kostant's problem for simple highest weight modules, in the case where the Lie algebra is of type A. Using this, we derive some old and new results which answer Kostant's problem in special cases. An easy sufficient condition derived from this criterion using Kazhdan-Lusztig combinatorics allows for a straightforward computational check using a computer, by which we get a complete answer for simple highest weight modules in the principal block of O for algebras of rank less than 5. In Paper III we relate the answer to Kostant's problem for certain modules to the answer to Kostant's problem for a module over a subalgebra. We also give a new description of a certain quotient of the dominant Verma module, which allows us to give a bound on the multiplicities of simple composition factors of primitive quotients of the universal enveloping algebra.

Estimation of elastic anisotropy, which is usually caused by rock fabrics and mineral orientation, has an important role in exploration seismology and better understanding of crustal seismic reflections. If not properly taken care of during processing steps, it may lead to wrong interpretation or distorted seismic image. In this thesis, a state-of-the-art under the development Laser Doppler Interferometer (LDI) device is used to measure phase velocities on the surface of rock samples from a major deformation zone (Österbybruk Deformation Zone) in the Bergslagen region of eastern Sweden. Then, a general inversion code is deployed to invert measured phase velocities to obtain full elastic stiffness tensors of two samples from the major deformation zone in the study area. At the end, results are used to correct for the anisotropy effects using three dimensionless Tsvankin's parameters and a non-hyperbolic moveout equation. The resulting stacked section shows partial reflection improvement of the deformation zone compared with the isotropic processing section. This suggests that rock anisotropy may also contribute to the generation of reflections from the deformation zones in the study area but requires further investigations.

The results of a solid-state 11B NMR study of a series of boronic acids, boronic esters, and boronic acid catechol cyclic esters with aromatic substituents are reported in this thesis. Boron-11 electric field gradient (EFG) and chemical shift (CS) tensors obtained from analyses of spectra acquired in magnetic fields of 9.4 T and 21.1 T are demonstrated to be useful for gaining insight into the molecular and electronic structure about the boron nucleus. It can be concluded that when adequate electronic variation is present in the compounds being studied, Ω is generally the most characteristic boron NMR parameter of the molecular and electronic environment for boronic acids and esters. Importantly, these data are only reliably accessible in ultrahigh magnetic fields. The experimental span values result from a delicate interplay of several competing factors, including hydrogen bonding, the value of the dihedral angle, and the type of aromatic ring system present.

This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital operator algebras A and B. Because of the different properties enjoyed by the two tensor products in connection to dilation theory, it is of interest to know when they coincide (completely isometrically). Motivated by earlier work due to Paulsen and Power, we provide conditions relating an operator algebra B and another family {C_i}_i of operator algebras under which, for any operator algebra A, the equality A ⊗_max B = A ⊗_min B either implies, or is implied by, the equalities A ⊗_max C_i = A ⊗_min C_i for every i. These results can be applied to the setting of a discrete group G pre-ordered by a subsemigroup G⁺, where B ⊆ C*_r(G) is the subalgebra of the reduced group C*-algebra of G generated by G⁺, and C_i = A(Q_i) are digraph algebras defined by considering certain pre-ordered subsets Q_i of G. The 16-dimensional algebra A₄ of real sedenions is obtained by applying the Cayley-Dickson doubling process to the real division algebra of octonions. The classification of subalgebras of A₄ up to conjugacy (i.e. by the action of the automorphism group of A₄) was completed in a previous investigation, except for the collection of those subalgebras which are isomorphic to the quaternions. We present a classification of quaternion subalgebras up to conjugacy.

In two separate studies, we used diffusion tensor imaging (DTI)to examine white matter changes secondary to traumatic brain injury (TBI) and spinal cord injury (SCI). The first study examined the utility of DTI for a single case diagnosis of mild TBI (mTBI) and demonstrated that the anterior limb of the internal capsule and the genu of the corpus callosum were sensitive and specific to mTBI. The second study examined the sub-acute effects of SCI on white matter tissue in the brain and demonstrated that SCI patients have a significantly greater degree of FA asymmetry than control subjects in the superior and posterior corona radiata. The first study has provided preliminary proof of principal evidence that DTI can be used to diagnose mTBI in individual cases. The second study suggests that the degree of asymmetry may be a useful biomarker for detecting subtle white matter changes.