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Surveys are commonly tailored to produce estimates of aggregate statistics with a desired level of precision. This may lead to very small sample sizes for subpopulations of interest, defined geographically or by content, which are not incorporated into the survey design. We refer to subpopulations where the sample size is too small to provide direct estimates with adequate precision as small areas or small domains. Despite the small sample sizes, reliable small area estimates are needed for economic and political decision making. Hence, model-based estimation techniques are used which increase the effective sample size by borrowing strength from other areas to provide accurate information for small areas. The paragraph above introduced small area estimation as a field of survey statistics where two conflicting philosophies of statistical inference meet: the design-based and the model-based approach. While the first approach is well suited for the precise estimation of aggregate statistics, the latter approach furnishes reliable small area estimates. In most applications, estimates for both large and small domains based on the same sample are needed. This poses a challenge to the survey planner, as the sampling design has to reflect different and potentially conflicting requirements simultaneously. In order to enable efficient design-based estimates for large domains, the sampling design should incorporate information related to the variables of interest. This may be achieved using stratification or sampling with unequal probabilities. Many model-based small area techniques require an ignorable sampling design such that after conditioning on the covariates the variable of interest does not contain further information about the sample membership. If this condition is not fulfilled, biased model-based estimates may result, as the model which holds for the sample is different from the one valid for the population. Hence, an optimisation of the sampling design without investigating the implications for model-based approaches will not be sufficient. Analogously, disregarding the design altogether and focussing only on the model is prone to failure as well. Instead, a profound knowledge of the interplay between the sample design and statistical modelling is a prerequisite for implementing an effective small area estimation strategy. In this work, we concentrate on two approaches to address this conflict. Our first approach takes the sampling design as given and can be used after the sample has been collected. It amounts to incorporate the survey design into the small area model to avoid biases stemming from informative sampling. Thus, once a model is validated for the sample, we know that it holds for the population as well. We derive such a procedure under a lognormal mixed model, which is a popular choice when the support of the dependent variable is limited to positive values. Besides, we propose a three pillar strategy to select the additional variable accounting for the design, based on a graphical examination of the relationship, a comparison of the predictive accuracy of the choices and a check regarding the normality assumptions.rnrnOur second approach to deal with the conflict is based on the notion that the design should allow applying a wide variety of analyses using the sample data. Thus, if the use of model-based estimation strategies can be anticipated before the sample is drawn, this should be reflected in the design. The same applies for the estimation of national statistics using design-based approaches. Therefore, we propose to construct the design such that the sampling mechanism is non-informative but allows for precise design-based estimates at an aggregate level.
Given a compact set K in R^d, the theory of extension operators examines the question, under which conditions on K, the linear and continuous restriction operators r_n:E^n(R^d)→E^n(K),f↦(∂^α f|_K)_{|α|≤n}, n in N_0 and r:E(R^d)→E(K),f↦(∂^α f|_K)_{α in N_0^d}, have a linear and continuous right inverse. This inverse is called extension operator and this problem is known as Whitney's extension problem, named after Hassler Whitney. In this context, E^n(K) respectively E(K) denote spaces of Whitney jets of order n respectively of infinite order. With E^n(R^d) and E(R^d), we denote the spaces of n-times respectively infinitely often continuously partially differentiable functions on R^d. Whitney already solved the question for finite order completely. He showed that it is always possible to construct a linear and continuous right inverse E_n for r_n. This work is concerned with the question of how the existence of a linear and continuous right inverse of r, fulfilling certain continuity estimates, can be characterized by properties of K. On E(K), we introduce a full real scale of generalized Whitney seminorms (|·|_{s,K})_{s≥0}, where |·|_{s,K} coincides with the classical Whitney seminorms for s in N_0. We equip also E(R^d) with a family (|·|_{s,L})_{s≥0} of those seminorms, where L shall be a a compact set with K in L-°. This family of seminorms on E(R^d) suffices to characterize the continuity properties of an extension operator E, since we can without loss of generality assume that E(E(K)) in D^s(L).
In Chapter 2, we introduce basic concepts and summarize the classical results of Whitney and Stein.
In Chapter 3, we modify the classical construction of Whitney's operators E_n and show that |E_n(·)|_{s,L}≤C|·|_{s,K} for s in[n,n+1).
In Chapter 4, we generalize a result of Frerick, Jordá and Wengenroth and show that LMI(1) for K implies the existence of an extension operator E without loss of derivatives, i.e. we have it fulfils |E(·)|_{s,L}≤C|·|_{s,K} for all s≥0. We show that a large class of self similar sets, which includes the Cantor set and the Sierpinski triangle, admits an extensions operator without loss of derivatives.
In Chapter 5 we generalize a result of Frerick, Jordá and Wengenroth and show that WLMI(r) for r≥1 implies the existence of a tame linear extension operator E having a homogeneous loss of derivatives, such that |E(·)|_{s,L}≤C|·|_{(r+ε)s,K} for all s≥0 and all ε>0.
In the last chapter we characterize the existence of an extension operator having an arbitrary loss of derivatives by the existence of measures on K.
The main socio-ecological pressures in five wetlands in the Greater Accra Region were first identified and then summarized by reviewing the relevant literature. As a second step, fieldwork in the region was carried out in 2016 to further examine the pressures identified in the literature. Most research on the wetlands in Ghana was published around the year 2000. Yet, similar socio-ecological pressures persist today. Based on both, fieldwork observations and the literature review, these pressures were ranked using the IUCN pressures system analysis framework. It is suggested that further research needs to proceed with uncovering how trade-offs between ecosystem and quality of life can be defined.
Early life adversity (ELA) is associated with a higher risk for diseases in adulthood. Changes in the immune system have been proposed to underlie this association. Although higher levels of inflammation and immunosenescence have been reported, data on cell-specific immune effects are largely absent. In addition, stress systems and health behaviors are altered in ELA, which may contribute to the generation of the "ELA immune phenotype". In this thesis, we have investigated the ELA immune phenotype on a cellular level and whether this is an indirect consequence of changes in behavior or stress reactivity. To address these questions the EpiPath cohort was established, consisting of 115 young adults with or without ELA. ELA participants had experienced separation from their parents in early childhood and were subsequently adopted, which is a standard model for ELA, whereas control participants grew up with their biological parents. At a first visit, blood samples were taken for analysis of epigenetic markers and immune parameters. A selection of the cohort underwent a standardized laboratory stress test (SLST). Endocrine, immune, and cardiovascular parameters were assessed at several time points before and after stress. At a second visit, participants underwent structural clinical interviews and filled out psychological questionnaires. We observed a higher number of activated T cells in ELA, measured by HLA-DR and CD25 expression. Neither cortisol levels nor health-risk behaviors explained the observed group differences. Besides a trend towards higher numbers of CCR4+CXCR3-CCR6+ CD4 T cells in ELA, relative numbers of immune cell subsets in circulation were similar between groups. No difference was observed in telomere length or in methylation levels of age-related CpGs in whole blood. However, we found a higher expression of senescence markers (CD57) on T cells in ELA. In addition, these cells had an increased cytolytic potential. A mediation analysis demonstrated that cytomegalovirus infection " an important driving force of immunosenescence " largely accounted for elevated CD57 expression. The psychological investigations revealed that after adoption, family conditions appeared to have been similar to the controls. However, PhD thesis MMC Elwenspoek 18 ELA participants scored higher on a depression index, chronic stress, and lower on self-esteem. Psychological, endocrine, and cardiovascular parameters significantly responded to the SLST, but were largely similar between the two groups. Only in a smaller subset of groups matched for gender, BMI, and age, the cortisol response seemed to be blunted in ELA participants. Although we found small differences in the methylation level of the GR promoter, GR sensitivity and mRNA expression levels GR as well as expression of the GR target genes FKBP5 and GILZ were similar between groups. Taken together, our data suggest an elevated state of immune activation in ELA, in which particularly T cells are affected. Furthermore, we found higher levels of T cells immunosenescence in ELA. Our data suggest that ELA may increase the risk of cytomegalovirus infection in early childhood, thereby mediating the effect of ELA on T cell specific immunosenescence. Importantly, we found no evidence of HPA dysregulation in participants exposed to ELA in the EpiPath cohort. Thus, the observed immune phenotype does not seem to be secondary to alterations in the stress system or health-risk behaviors, but rather a primary effect of early life programming on immune cells. Longitudinal studies will be necessary to further dissect cause from effect in the development of the ELA immune phenotype.
There are large health, societal, and economic costs associated with attrition from psychological services. The recently emerged, innovative statistical tool of complex network analysis was used in the present proof-of-concept study to improve the prediction of attrition. Fifty-eight patients undergoing psychological treatment for mood or anxiety disorders were assessed using Ecological Momentary Assessments four times a day for two weeks before treatment (3,248 measurements). Multilevel vector autoregressive models were employed to compute dynamic symptom networks. Intake variables and network parameters (centrality measures) were used as predictors for dropout using machine-learning algorithms. Networks for patients differed significantly between completers and dropouts. Among intake variables, initial impairment and sex predicted dropout explaining 6% of the variance. The network analysis identified four additional predictors: Expected force of being excited, outstrength of experiencing social support, betweenness of feeling nervous, and instrength of being active. The final model with the two intake and four network variables explained 32% of variance in dropout and identified 47 out of 58 patients correctly. The findings indicate that patients" dynamic network structures may improve the prediction of dropout. When implemented in routine care, such prediction models could identify patients at risk for attrition and inform personalized treatment recommendations.
Die räumliche Entwicklung von Städten und Regionen wird durch Trends wie Klimawandel, demographische Veränderungen und Strukturwandel beeinflusst, welche nicht an Verwaltungsgrenzen aufhören, sondern die Entwicklung großflächiger Gebiete bestimmen. Außerdem weisen Grenzräume häufig funktionale und thematische Verflechtungen auf, die über die nationalen Grenzen hinweg bestehen. Damit verbunden sind ein regelmäßiger Austausch und Abhängigkeiten zwischen Grenzräumen und deren Bewohnern. Daher ist die Koordination der grenzüberschreitenden Raumentwicklung entscheidend für eine zukunftsorientierte und nachhaltige räumliche Entwicklung. Aufgrund seiner hohen Bedeutung wird dieses Thema von europäischen Wissenschaftlern in der ersten Ausgabe der Themenhefte Borders in Perspective aus verschiedenen Perspektiven beleuchtet.
This thesis considers the general task of computing a partition of a set of given objects such that each set of the partition has a cardinality of at least a fixed number k. Among such kinds of partitions, which we call k-clusters, the objective is to find the k-cluster which minimises a certain cost derived from a given pairwise difference between objects which end up the same set. As a first step, this thesis introduces a general problem, denoted by (||.||,f)-k-cluster, which models the task to find a k-cluster of minimum cost given by an objective function computed with respect to specific choices for the cost functions f and ||.||. In particular this thesis considers three different choices for f and also three different choices for ||.|| which results in a total of nine different variants of the general problem. Especially with the idea to use the concept of parameterised approximation, we first investigate the role of the lower bound on the cluster cardinalities and find that k is not a suitable parameter, due to remaining NP-hardness even for the restriction to the constant 3. The reductions presented to show this hardness yield the even stronger result which states that polynomial time approximations with some constant performance ratio for any of the nine variants of (||.||,f)-k-cluster require a restriction to instances for which the pairwise distance on the objects satisfies the triangle inequality. For this restriction to what we informally refer to as metric instances, constant-factor approximation algorithms for eight of the nine variants of (||.||,f)-k-cluster are presented. While two of these algorithms yield the provably best approximation ratio (assuming P!=NP), others can only guarantee a performance which depends on the lower bound k. With the positive effect of the triangle inequality and applications to facility location in mind, we discuss the further restriction to the setting where the given objects are points in the Euclidean metric space. Considering the effect of computational hardness caused by high dimensionality of the input for other related problems (curse of dimensionality) we check if this is also the source of intractability for (||.||,f)-k-cluster. Remaining NP-hardness for restriction to small constant dimensionality however disproves this theory. We then use parameterisation to develop approximation algorithms for (||.||,f)-k-cluster without restriction to metric instances. In particular, we discuss structural parameters which reflect how much the given input differs from a metric. This idea results in parameterised approximation algorithms with parameters such as the number of conflicts (our name for pairs of objects for which the triangle inequality is violated) or the number of conflict vertices (objects involved in a conflict). The performance ratios of these parameterised approximations are in most cases identical to those of the approximations for metric instances. This shows that for most variants of (||.||,f)-k-cluster efficient and reasonable solutions are also possible for non-metric instances.
At any given moment, our senses are assaulted with a flood of information from the environment around us. We need to pick our way through all this information in order to be able to effectively respond to that what is relevant to us. In most cases we are usually able to select information relevant to our intentions from what is not relevant. However, what happens to the information that is not relevant to us? Is this irrelevant information completely ignored so that it does not affect our actions? The literature suggests that even though we mayrnignore an irrelevant stimulus, it may still interfere with our actions. One of the ways in which irrelevant stimuli can affect actions is by retrieving a response with which it was associated. An irrelevant stimulus that is presented in close temporal contiguity with a relevant stimulus can be associated with the response made to the relevant stimulus " an observation termed distractor-response binding (Rothermund, Wentura, & De Houwer, 2005). The studies presented in this work take a closer look at such distractor-response bindings, and therncircumstances in which they occur. Specifically, the study reported in chapter 6 examined whether only an exact repetition of the distractor can retrieve the response with which it was associated, or whether even similar distractors may cause retrieval. The results suggested that even repeating a similar distractor caused retrieval, albeit less than an exact repetition. In chapter 7, the existence of bindings between a distractor and a response were tested beyond arnperceptual level, to see whether they exist at an (abstract) conceptual level. Similar to perceptual repetition, distractor-based retrieval of the response was observed for the repetition of concepts. The study reported in chapter 8 of this work examined the influence of attention on the feature-response binding of irrelevant features. The results pointed towards a stronger binding effects when attention was directed towards the irrelevant feature compared to whenrnit was not. The study in chapter 9 presented here looked at the processes underlying distractor-based retrieval and distractor inhibition. The data suggest that motor processes underlie distractor-based retrieval and cognitive process underlie distractor inhibition. Finally, the findings of all four studies are also discussed in the context of learning.
We will consider discrete dynamical systems (X,T) which consist of a state space X and a linear operator T acting on X. Given a state x in X at time zero, its state at time n is determined by the n-th iteration T^n(x). We are interested in the long-term behaviour of this system, that means we want to know how the sequence (T^n (x))_(n in N) behaves for increasing n and x in X. In the first chapter, we will sum up the relevant definitions and results of linear dynamics. In particular, in topological dynamics the notions of hypercyclic, frequently hypercyclic and mixing operators will be presented. In the setting of measurable dynamics, the most important definitions will be those of weakly and strongly mixing operators. If U is an open set in the (extended) complex plane containing 0, we can define the Taylor shift operator on the space H(U) of functions f holomorphic in U as Tf(z) = (f(z)- f(0))/z if z is not equal to 0 and otherwise Tf(0) = f'(0). In the second chapter, we will start examining the Taylor shift on H(U) endowed with the topology of locally uniform convergence. Depending on the choice of U, we will study whether or not the Taylor shift is weakly or strongly mixing in the Gaussian sense. Next, we will consider Banach spaces of functions holomorphic on the unit disc D. The first section of this chapter will sum up the basic properties of Bergman and Hardy spaces in order to analyse the dynamical behaviour of the Taylor shift on these Banach spaces in the next part. In the third section, we study the space of Cauchy transforms of complex Borel measures on the unit circle first endowed with the quotient norm of the total variation and then with a weak-* topology. While the Taylor shift is not even hypercyclic in the first case, we show that it is mixing for the latter case. In Chapter 4, we will first introduce Bergman spaces A^p(U) for general open sets and provide approximation results which will be needed in the next chapter where we examine the Taylor shift on these spaces on its dynamical properties. In particular, for 1<=p<2 we will find sufficient conditions for the Taylor shift to be weakly mixing or strongly mixing in the Gaussian sense. For p>=2, we consider specific Cauchy transforms in order to determine open sets U such that the Taylor shift is mixing on A^p(U). In both sections, we will illustrate the results with appropriate examples. Finally, we apply our results to universal Taylor series. The results of Chapter 5 about the Taylor shift allow us to consider the behaviour of the partial sums of the Taylor expansion of functions in general Bergman spaces outside its disc of convergence.
The forward effect of testing refers to the finding that retrieval practice of previously studied information increases retention of subsequently studied other information. It has recently been hypothesized that the forward effect (partly) reflects the result of a reset-of-encoding (ROE) process. The proposal is that encoding efficacy decreases with an increase in study material, but testing of previously studied information resets the encoding process and makes the encoding of the subsequently studied information as effective as the encoding of the previously studied information. The goal of the present study was to verify the ROE hypothesis on an item level basis. An experiment is reported that examined the effects of testing in comparison to restudy on items’ serial position curves. Participants studied three lists of items in each condition. In the testing condition, participants were tested immediately on non-target lists 1 and 2, whereas in the restudy condition, they restudied lists 1 and 2. In both conditions, participants were tested immediately on target list 3. Influences of condition and items’ serial learning position on list 3 recall were analyzed. The results showed the forward effect of testing and furthermore that this effect varies with items’ serial list position. Early target list items at list primacy positions showed a larger enhancement effect than middle and late target list items at non-primacy positions. The results are consistent with the ROE hypothesis on an item level basis. The generalizability of the ROE hypothesis across different experimental tasks, like the list-method directed-forgetting task, is discussed.