Approximation of multi-variable signals and systems : a tensor decomposition approach

Signals that evolve over multiple variables or indices occur in all fields of science and engineering. Measurements of the distribution of temperature across the globe during a certain period of time are an example of such a signal. Multivariable systems describe the evolution of signals over a spatial-temporal domain. The mathematical equations involved in such a description are called a model and this model dictates which values the signals can obtain as a function of time and space. In an industrial production setting, such mathematical models may be used to monitor the process or determine the control action required to reach a certain set-point. Since their evolution is over both space and time, multi-variable systems are described by Partial Differential Equations (PDEs). Generally, it is not the signals or systems themselves one is interested in, but the information they carry. The main numerical tools to extract system trajectories from the PDE description are Finite Element (FE) methods. FE models allow simulation of the model via a discretization scheme. The main problem with FE models is their complexity, which leads to large simulation time, making them not suitable for applications such as on-line monitoring of the process or model-based control design. Model reduction techniques aim to derive lowcomplexity replacement models from complex process models, in the setting of this work, from FE models. The approximations are achieved by projection on lower-dimensional subspaces of the signals and their dynamic laws. This work considers the computation of empirical projection spaces for signals and systems evolving over multi-dimensional domains. Formally, signal approximation may be viewed as a low-rank approximation problem. Whenever the signal under consideration is a function of multiple variables, low-rank approximations can be obtained via multi-linear functionals, tensors. It has been explained in this work that approximation of multi-variable systems also boils down to low-rank approximation problems.The first problem under consideration was that of finding low-rank approximations to tensors. For order-2 tensors, matrices, this problem is well understood. Generalization of these results to higher-order tensors is not straightforward. Finding tensor decompositions that allow suitable approximations after truncation is an active area of research. In this work a concept of rank for tensors, referred to as multi-linear or modal rank, has been considered. A new method has been defined to obtain modal rank decompositions to tensors, referred to as Tensor Singular Value Decomposition (TSVD). Properties of the TSVD that reflect its sparsity structure have been derived and low-rank approximation error bounds have been obtained for certain specific cases. An adaptation of the TSVD method has been proposed that may give better approximation results when not all modal directions are approximated. A numerical algorithm has been presented for the computation of the (dedicated) TSVD, which with a small adaptation can also be used to compute successive rank-one approximation to tensors. Finally, a simulation example has been included which demonstrates the methods proposed in this work and compares them to a well-known existing method. The concepts that were introduced and discussed with regard to signal approximation have been used in a system approximation context.We have considered the well-known model reduction method of Proper Orthogonal Decompositions (POD). We have shown how the basis functions inferred from the TSVD can be used to define projection spaces in POD. This adaptation is both a generalization and a restriction. It is a generalization because it allows POD to be used in a scalable fashion for problems with an arbitrary number of dependent and independent variables. However, it is also a restriction, since the projection spaces require a Cartesian product structure of the domain. The model reduction method that is thus obtained has been demonstrated on a benchmark example from chemical engineering. This application shows that the method is indeed feasible, and that the accuracy is comparable to existing methods for this example. In the final part of the thesis the problem of reconstruction and approximation of multi-dimensional signals was considered. Specifically, the problem of sampling and signal reconstruction for multi-variable signals with non-uniformly distributed sensors on a Cartesian domain has been considered. The central question of this chapter was that of finding a reconstruction of the original signal from its samples. A specific reconstruction map has been examined and conditions for exact reconstruction have been presented. In case that exact reconstruction was not possible, we have derived an expression for the reconstruction error

Critical Success Factors of Continuous Practices in a DevOps Context

Context: Software companies try to achieve adaptive near to real-time software delivery and apply continuous practices in a DevOps context. While continuous practices may create new business opportunities, continuous practices also present new challenges. Objective: This study aims to aid in adopting continuous practices and performance improvements by increasing our understanding of these practices in a DevOps context. Method: By conducting a systematic literature review we identified critical success factors on continuous practices and grouped the found factors. This led to the construction of our initial framework. We started to validate the critical success factors in this framework in a DevOps context by conducting a first pilot interview. Results: We developed an initial framework of critical success factors and conducted a pilot interview to make a first step to validate the framework. Some factors were confirmed and clarified i.e., enriched, on the basis of the retrieved information. In future work we will strive at further validation of the framework. Conclusions: We took a first step to validate our framework and retrieved valuable information, which is promising to take the next steps for further development of the framework

Bekehrung als leibliche Identität: Versuch einer kulturpsychologischen Interpretation eines religiösen Phänomens am Beispiel der "alt-reformierten" Minderheit in den Niederlanden

Es wird argumentiert, dass die Kulturpsychologie zurzeit in unterschiedlichen Formen ein "comeback" erlebt, das gerade für die psychologische Erforschung der Religion neue Chancen bietet. Anhand des Beispiels einer religiös-kulturellen Minderheit in den Niederlanden wird gezeigt, wie die Lebensform, in die der Mensch jeweils eingebettet ist, Verhalten, Erkennen und Erfahren konstituiert und konstruiert. Verwendete Perspektiven sind unter anderem die rhetorisch-responsive Version des Sozialkonstruktionismus und der Habitusbegriff von P. Bourdieu

Historisierende Ansätze in einer Kulturpsychologie der Religion: Plädoyer für Interdisziplinarität

Nach einer kurzen Schilderung des Auflebens der Religionspsychologie in jüngster Zeit wird eine Orientierung auf die hermeneutischen Psychologien als diejenigen Ansätze in der Psychologie, die dem Forschungsobjekt am adäquatesten sind, vorgeschlagen. Da Religiosität ein kulturell konstituiertes Phänomen ist, das von der Psychologie in einer individualisierenden historischen Perspektive zu verstehen ist, wird eine kulturpsychologische Perspektive vorgestellt, deren diachrone Variante und deren Beziehungen zur Religionspsychologie näher dargestellt werden. Als Beispiel interdisziplinärer Forschung wird die psychohistorisch arbeitende Religionspsychologie ausgeführt. Abschließend wird kurz auf weitere Möglichkeiten eines Ausbaus der Religionspsychologie hingewiesen

Coeliac disease : investigation of the genetic factors underlying coeliac disease

Coeliac disease is a common food intolerance with a complex genetic aetiology. It is caused by ingestion of gluten peptides from wheat and related proteins from barley and rye in genetically susceptible individuals. The disease affects the small intestine and leads to abnormalities ranging from the infiltration of the villous epithelium by lymphocytes to total villous atrophy. Clinical symptoms include gastrointestinal complaints such as diarrhoea and abdominal pain but also fatigue, weight loss, anaemia, osteopenia, growth retardation and failure to thrive. Coeliac disease is treated by a life-long gluten-free diet; there is no drug therapy available. One important genetic factor contributing to coeliac disease is the human leukocyte antigen (HLA) DQ locus. The majority of patients are positive for DQ2, and almost all of the remaining patients are positive for DQ8. However, the contribution of the HLA region comprises at most half of the total genetic risk. Therefore, non-HLA genes must also play an important role in coeliac disease pathogenesis, but little is known about the location and identity of these genes. This thesis describes the first localisation of susceptibility loci for coeliac disease in the Dutch population, in a well-characterized set of affected sibpairs. Linkage analysis revealed that a major locus was located at 19p13.1. This is the first locus to reach genome-wide significance in coeliac disease in an outbred population. Another locus, showing genome-wide suggestive linkage, was identified at 6q21-22. This region is also implicated in other autoimmune disorders and it may therefore harbour a general susceptibility gene for autoimmunity. Both the 19p13.1 and 6q21-22 loci present novel susceptibility loci for coeliac disease. A second genome-wide screen was performed in a four-generation Dutch family with 17 coeliac disease patients. Surprisingly, a third locus, located at 9p21-13, was identified as the major locus in this family. This locus had also been implicated in Scandinavian families with coeliac disease, and probably presents a locus with a small risk to coeliac disease in general. The 19p13.1 candidate region of 3 Mb, containing 92 genes, was subjected to systematic fine-mapping. Association analysis using microsatellite markers narrowed-down the region to 450 kb and only 12 genes. Subsequent typing of single nucleotide polymorphisms pinpointed the location of the gene to the final 150 kb of this region, with eight possible candidate genes left. Furthermore, the contribution of three functional candidate genes to coeliac disease risk was evaluated: 1. tissue transglutaminase, which modifies gluten peptides into epitopes with strong affinity for HLA-DQ2 and DQ8, resulting in a greatly enhanced T cell response, 2. the cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), which has been implicated as a general susceptibility gene for autoimmunity, 3. the cytokine interferon-?, which plays an important role in the pathogenesis of coeliac disease. However, none of these genes showed association with coeliac disease. Finally, an extensive scan of the HLA region was performed to search additional HLA risk loci for coeliac disease, acting independently of DQ2. The results indicated that the contribution of the HLA region is mainly attributable to DQ2 and that a significant contribution of other HLA genes is unlikely

Algal-Induced Biogeomorphic Feedbacks Lay the Groundwork for Coastal Wetland Development

Ecosystem establishment under adverse geophysical conditions is often studied within the “windows of opportunity” framework, identifying disturbance-free periods (e.g., calm wave climate) where species can overcome establishment thresholds. However, the role of biogeophysical interactions in this framework is less well understood. The establishment of saltmarsh vegetation on tidal flats, for example, is limited by abiotic factors such as hydrodynamics, sediment stability and drainage. On tidal flats, raised sediment ridges colonized by algal mats (Vaucheria sp.) appear to accomodate high densities of plant seedlings. Such ridges were previously found to have higher sediment strength than substratum without algae. Here, we investigate whether these measurements can be explained by geophysical factors only, or that biological (Vaucheria-induced) processes influence tidal marsh establishment by forming stabilized bedforms. We performed two experiments under controlled mesocosm conditions, to test the hypotheses that (a) Vaucheria grows better on elevated topographic relief, that (b) the binding force of their algal filaments increases sediment strength, and that (c) Vaucheria consequently creates elevated topographic relief that further facilitates algal growth. Our experimental results confirm the existence of this algal-induced biogeomorphic feedback cycle. These findings imply that benthic algae like Vaucheria may contribute significantly to tidal marsh formation by creating elevated and stabilized substratum. This suggests biogeophysical feedbacks can “widen” the windows of opportunity for further ecosystem establishment. Our results could be useful for the design of managed realignment projects aimed at restoring the unique ecosystem services of coastal wetlands, such as habitat biodiversity, carbon sequestration potential and nature-based flood defense