Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

The prehistoric inhabitants of the Wadi Howar : an anthropological study of human skeletal remains from the Sudanese part of the Eastern Sahara

All currently available human skeletal remains from the Wadi Howar (Eastern Sahara, Sudan) were employed in an anthropological study. The study’s first aim was to describe this unique 5th to 2nd millennium BCE material, which comprised representatives of all three prehistoric occupation phases of the region. Detecting diachronic differences in robusticity, occupational stress levels and health within the spatially, temporally and culturally heterogeneous sample was its second objective. The study’s third goal was to reveal metric and non-metric affinities between the different parts of the series and between the Wadi Howar material and other relevant prehistoric as well as modern African populations. rnThe reconstruction and comprehensive osteological analysis of 23 as yet unpublished individuals, the bulk of the Wadi Howar series, constituted the first stage of the study. The analyses focused on each individual’s in situ position, state of preservation, sex, age at death, living height, living weight, physique, biological ancestry, epigenetic traits, robusticity, occupational stress markers, health and metric as well as morphological characteristics. Building on the results of these efforts and the re-examination of the rest of the material, the Wadi Howar series as a whole, altogether 32 individuals, could be described. rnA wide variety of robusticity, occupational stress and health variables was evaluated. The pre-Leiterband (hunter-gatherer-fisher/hunter-gatherer-fisher-herder) and the Leiterband (herder-gatherer) data of over a third of these variables differed statistically significantly or in tendency from each other. The Leiterband sub-sample was characterised by higher enamel hypoplasia frequencies, lower mean ages at death and less pronounced expressions of occupational stress traits. This pattern was interpreted as evidence that the adoption and intensification of animal husbandry did probably not constitute reactions to worsening conditions. Apart from that, the relevant observations, noteworthy tendencies and significant differences were explained as results of a broader spectrum of pre-Leiterband subsistence activities and the negative side effects of the increasingly specialised herder-gatherer economy of the Leiterband phase. rnUsing only the data which could actually be collected from it, multiple, separate, individualised discriminant function analyses were carried out for each Wadi Howar skeleton to determine which prehistoric and which modern comparative sample it was most similar to. The results of all individual analyses were then summarised and examined as a whole. Thus it became possible to draw conclusions about the affinities the Wadi Howar material shared with prehistoric as well as modern populations and to answer questions concerning the diachronic links between the Wadi Howar’s prehistoric populations. When the Wadi Howar remains were positioned in the context of the selected prehistoric (Jebel Sahaba/Tushka, A-Group, Malian Sahara) and modern comparative samples (Southern Sudan, Chad, Mandinka, Somalis, Haya) in this fashion three main findings emerged. Firstly, the series as a whole displayed very strong affinities with the prehistoric sample from the Malian Sahara (Hassi el Abiod, Kobadi, Erg Ine Sakane, etc.) and the modern material from Southern Sudan and, to a lesser extent, Chad. Secondly, the pre-Leiterband and the Leiterband sub-sample were closer to the prehistoric Malian as well as the modern Southern Sudanese material than they were to each other. Thirdly, the group of pre-Leiterband individuals approached the Late Pleistocene sample from Jebel Sahaba/Tushka under certain circumstances. A theory offering explanations for these findings was developed. According to this theory, the entire prehistoric population of the Wadi Howar belonged to a Saharo-Nilotic population complex. The Jebel Sahaba/Tushka population constituted an old Nilotic and the early population of the Malian Sahara a younger Saharan part of this complex. The pre-Leiterband groups probably colonised the Wadi Howar from the east, either during or soon after the original Saharo-Nilotic expansion. Unlike the pre-Leiterband groups, the Leiterband people originated somewhere west of the Wadi Howar. They entered the region in the context of a later, secondary Saharo-Nilotic expansion. In the process, the incoming Leiterband groups absorbed many members of the Wadi Howar’s older pre-Leiterband population. The increasing aridification of the Wadi Howar region ultimately forced its prehistoric inhabitants to abandon the wadi. Most of them migrated south and west. They, or groups closely related to them, probably were the ancestors of the majority of the Nilo-Saharan-speaking pastoralists of modern-day Southern Sudan and Eastern Chad.

Context-dependent interpretation of the conjunction 'und' in different age-groups

In contrast to formal semantics, the conjunction and is nonsymmetrical in pragmatics. The events in Marc went to bed and fell asleep seem to have occurred chronologically although no explicit time reference is given. As the temporal interpretation appears to be weaker in Mia ate chocolate and drank milk, it seems that the kind and nature of events presented in a context influences the interpretation of the conjunction. This work focuses on contextual influences on the interpretation of the German conjunction und (‘and’). A variety of theoretic approaches are concerned with whether and contributes to the establishment of discourse coherence via pragmatic processes or whether the conjunction has complex semantic meaning. These approaches are discussed with respect to how they explain the temporal and additive interpretation of the conjunction and the role of context in the interpre-tation process. It turned out that most theoretic approaches do not consider the importance of different kinds of context in the interpretation process.rnIn experimental pragmatics there are currently only very few studies that investigate the inter-pretation of the conjunction. As there are no studies that investigate contextual influences on the interpretation of und systematically or investigate preschoolers interpretation of the con-junction, research questions such as How do (preschool) children interpret ‘und’? and Does the kind of events conjoined influence children’s and adults’ interpretation? are yet to be answered. Therefore, this dissertation systematically investigates how different types of context influence children’s interpretation of und. Three auditory comprehension studies were conducted in German. Of special interest was whether and how the order of events introduced in a context contributes to the temporal read-ing of the conjunction und. Results indicate that the interpretation of und is – at least in Ger-man – context-dependent: The conjunction is interpreted temporally more often when events that typical occur in a certain order are connected (typical contexts) compared to events with-out typical event order (neutral contexts). This suggests that the type of events conjoined in-fluences the interpretation process. Moreover, older children and adults interpret the conjunc-tion temporally more often than the younger cohorts if the conjoined events typically occur in a certain order. In neutral contexts, additive interpretations increase with age. 5-year-olds reject reversed order statements more often in typical contexts compared to neutral contexts. However, they have more difficulties with reversed order statements in typical contexts where they perform at chance level. This suggests that not only the type of event but also other age-dependent factors such as knowledge about scripts influence children’s performance. The type of event conjoined influences children’s and adults’ interpretation of the conjunction. There-fore, the influence of different event types and script knowledge on the interpretation process does not only have to be considered in future experimental studies on language acquisition and pragmatics but also in experimental pragmatics in general. In linguistic theories, context has to be given a central role and a commonly agreed definition of context that considers the consequences arising from different event types has to be agreed upon.

Detrimental effects of exuberant and restrained immune responses against the central nervous system in the context of multiple sclerosis and glioblastoma multiforme

Glioblastoma multiforme (GBM) is the most common and most aggressive astrocytic tumor of the central nervous system (CNS) in adults. The standard treatment consisting of surgery, followed by a combinatorial radio- and chemotherapy, is only palliative and prolongs patient median survival to 12 to 15 months. The tumor subpopulation of stem cell-like glioma-initiating cells (GICs) shows resistance against radiation as well as chemotherapy, and has been suggested to be responsible for relapses of more aggressive tumors after therapy. The efficacy of immunotherapies, which exploit the immune system to specifically recognize and eliminate malignant cells, is limited due to strong immunosuppressive activities of the GICs and the generation of a specialized protective microenvironment. The molecular mechanisms underlying the therapy resistance of GICs are largely unknown. rnThe first aim of this study was to identify immune evasion mechanisms in GICs triggered by radiation. A model was used in which patient-derived GICs were treated in vitro with fractionated ionizing radiation (2.5 Gy in 7 consecutive passages) to select for a more radio-resistant phenotype. In the model cell line 1080, this selection process resulted in increased proliferative but diminished migratory capacities in comparison to untreated control GICs. Furthermore, radio-selected GICs downregulated various proteins involved in antigen processing and presentation, resulting in decreased expression of MHC class I molecules on the cellular surface and diminished recognition potential by cytotoxic CD8+ T cells. Thus, sub-lethal fractionated radiation can promote immune evasion and hamper the success of adjuvant immunotherapy. Among several immune-associated proteins, interferon-induced transmembrane protein 3 (IFITM3) was found to be upregulated in radio-selected GICs. While high expression of IFITM3 was associated with a worse overall survival of GBM patients (TCGA database) and increased proliferation and migration of differentiated glioma cell lines, a strong contribution of IFITM3 to proliferation in vitro as well as tumor growth and invasiveness in a xenograft model could not be observed. rnMultiple sclerosis (MS) is the most common autoimmune disease of the CNS in young adults of the Western World, which leads to progressive disability in genetically susceptible individuals, possibly triggered by environmental factors. It is assumed that self-reactive, myelin-specific T helper cell 1 (Th1) and Th17 cells, which have escaped the control mechanisms of the immune system, are critical in the pathogenesis of the human disease and its animal model experimental autoimmune encephalomyelitis (EAE). It was observed that in vitro differentiated interleukin 17 (IL-17) producing Th17 cells co-expressed the Th1-phenotypic cytokine Interferon-gamma (IFN-γ) in combination with the two respective lineage-associated transcription factors RORγt and T-bet after re-isolation from the CNS of diseased mice. Pathogenic molecular mechanisms that render a CD4+ T cell encephalitogenic have scarcely been investigated up to date. rnIn the second part of the thesis, whole transcriptional changes occurring in in vitro differentiated Th17 cells in the course of EAE were analyzed. Evaluation of signaling networks revealed an overrepresentation of genes involved in communication between the innate and adaptive immune system and metabolic alterations including cholesterol biosynthesis. The transcription factors Cebpa, Fos, Klf4, Nfatc1 and Spi1, associated with thymocyte development and naïve T cells were upregulated in encephalitogenic CNS-isolated CD4+ T cells, proposing a contribution to T cell plasticity. Correlation of the murine T-cell gene expression dataset to putative MS risk genes, which were selected based on their proximity (± 500 kb; ensembl database, release 75) to the MS risk single nucleotide polymorphisms (SNPs) proposed by the most recent multiple sclerosis GWAS in 2011, revealed that 67.3% of the MS risk genes were differentially expressed in EAE. Expression patterns of Bach2, Il2ra, Irf8, Mertk, Odf3b, Plek, Rgs1, Slc30a7, and Thada were confirmed in independent experiments, suggesting a contribution to T cell pathogenicity. Functional analysis of Nfatc1 revealed that Nfatc1-deficient CD4+ T cells were restrained in their ability to induce clinical signs of EAE. Nfatc1-deficiency allowed proper T cell activation, but diminished their potential to fully differentiate into Th17 cells and to express high amounts of lineage cytokines. As the inducible Nfatc1/αA transcript is distinct from the other family members, it could represent an interesting target for therapeutic intervention in MS.rn