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The thesis looks at the question asking for the computability of the dot-depth of star-free regular languages. Here one has to determine for a given star-free regular language the minimal number of alternations between concatenation on one hand, and intersection, union, complement on the other hand. This question was first raised in 1971 (Brzozowski/Cohen) and besides the extended star-heights problem usually refered to as one of the most difficult open questions on regular languages. The dot-depth problem can be captured formally by hierarchies of classes of star-free regular languages B(0), B(1/2), B(1), B(3/2),... and L(0), L(1/2), L(1), L(3/2),.... which are defined via alternating the closure under concatenation and Boolean operations, beginning with single alphabet letters. Now the question of dot-depth is the question whether these hierarchy classes have decidable membership problems. The thesis makes progress on this question using the so-called forbidden pattern approach: Classes of regular languages are characterized in terms of patterns in finite automata (subgraphs in the transition graph) that are not allowed. Such a characterization immediately implies the decidability of the respective class, since the absence of a certain pattern in a given automaton can be effectively verified. Before this work, the decidability of B(0), B(1/2), B(1) and L(0), L(1/2), L(1), L(3/2) were known. Here a detailed study of these classes with help of forbidden patterns is given which leads to new insights into their inner structure. Furthermore, the decidability of B(3/2) is proven. Based on these results a theory of pattern iteration is developed which leads to the introduction of two new hierarchies of star-free regular languages. These hierarchies are decidable on one hand, on the other hand they are in close connection to the classes B(n) and L(n). It remains an open question here whether they may in fact coincide. Some evidence is given in favour of this conjecture which opens a new way to attack the dot-depth problem. Moreover, it is shown that the class L(5/2) is decidable in the restricted case of a two-letter alphabet.
In this thesis we investigate near-isomorphism classes and isomorphism classes of almost completely decomposable groups. In Chapter 2 we introduce the concept of almost completely decomposable groups and sum up their most important facts. A local group is an almost completely decomposable group with a primary regulator quotient. A uniform group is a rigid local group with a homocyclic regulator quotient. In Chapter 3 a weakening of isomorphism, called type-isomorphism, appears. It is shown that type-isomorphism agrees with Lady's near-isomorphism. By the Main Decomposition Theorem and the Primary Reduction Theorem we are allowed to restrict ourselves on clipped local groups, namely groups without a direct rank-one summand. In Chapter 4 we collect facts of matrices over commutative rings with an identity element. Matrices over the local ring (Z / p^e Z) of residue classes of the rational integers modulo a prime power play an important role. In Chapter 5 we introduce representing matrices of finite essential extensions. Here a normal form for local groups is found by the Gauß algorithm. Uniform groups have representing matrices in Hermite normal form. The classification problems for almost completely decomposable groups up to isomorphism and up to near-isomorphism can be rephrased as equivalence problems for the representing matrices. In Chapter 6 we derive a criterion for the representing matrices of local groups in Gauß normal form. In Chapter 7 we formulate the matrix criterion for uniform groups. Two representing matrices in Hermite normal form describe isomorphic groups if and only if the rest blocks of the representing matrices are T-diagonally equivalent. Starting from a fixed near-isomorphism class in Chapter 8 we investigate isomorphism classes of uniform groups. We count groups and isomorphism classes. In Chapter 9 we specialize on uniform groups of rank 2r with a regulator quotient of rank r such that the rest block of the representing matrix is invertible and normed.
Complexity and Partitions
(2001)
Computational complexity theory usually investigates the complexity of sets, i.e., the complexity of partitions into two parts. But often it is more appropriate to represent natural problems by partitions into more than two parts. A particularly interesting class of such problems consists of classification problems for relations. For instance, a binary relation R typically defines a partitioning of the set of all pairs (x,y) into four parts, classifiable according to the cases where R(x,y) and R(y,x) hold, only R(x,y) or only R(y,x) holds or even neither R(x,y) nor R(y,x) is true. By means of concrete classification problems such as Graph Embedding or Entailment (for propositional logic), this thesis systematically develops tools, in shape of the boolean hierarchy of NP-partitions and its refinements, for the qualitative analysis of the complexity of partitions generated by NP-relations. The Boolean hierarchy of NP-partitions is introduced as a generalization of the well-known and well-studied Boolean hierarchy (of sets) over NP. Whereas the latter hierarchy has a very simple structure, the situation is much more complicated for the case of partitions into at least three parts. To get an idea of this hierarchy, alternative descriptions of the partition classes are given in terms of finite, labeled lattices. Based on these characterizations the Embedding Conjecture is established providing the complete information on the structure of the hierarchy. This conjecture is supported by several results. A natural extension of the Boolean hierarchy of NP-partitions emerges from the lattice-characterization of its classes by considering partition classes generated by finite, labeled posets. It turns out that all significant ideas translate from the case of lattices. The induced refined Boolean hierarchy of NP-partitions enables us more accuratly capturing the complexity of certain relations (such as Graph Embedding) and a description of projectively closed partition classes.
Starfree regular languages can be build up from alphabet letters by using only Boolean operations and concatenation. The complexity of these languages can be measured with the so-called dot-depth. This measure leads to concatenation hierarchies like the dot-depth hierarchy (DDH) and the closely related Straubing-Thérien hierarchy (STH). The question whether the single levels of these hierarchies are decidable is still open and is known as the dot-depth problem. In this thesis we prove/reprove the decidability of some lower levels of both hierarchies. More precisely, we characterize these levels in terms of patterns in finite automata (subgraphs in the transition graph) that are not allowed. Therefore, such characterizations are called forbidden-pattern characterizations. The main results of the thesis are as follows: forbidden-pattern characterization for level 3/2 of the DDH (this implies the decidability of this level) decidability of the Boolean hierarchy over level 1/2 of the DDH definition of decidable hierarchies having close relations to the DDH and STH Moreover, we prove/reprove the decidability of the levels 1/2 and 3/2 of both hierarchies in terms of forbidden-pattern characterizations. We show the decidability of the Boolean hierarchies over level 1/2 of the DDH and over level 1/2 of the STH. A technique which uses word extensions plays the central role in the proofs of these results. With this technique it is possible to treat the levels 1/2 and 3/2 of both hierarchies in a uniform way. Furthermore, it can be used to prove the decidability of the mentioned Boolean hierarchies. Among other things we provide a combinatorial tool that allows to partition words of arbitrary length into factors of bounded length such that every second factor u leads to a loop with label u in a given finite automaton.
A completely decomposable group is a direct sum of subgroups of the rationals. An almost completely decomposable group is a torsion free abelian group that contains a completely decomposable group as subgroup of finite index. Tight subgroups are maximal subgroups (with respect to set inclusion) among the completely decomposable subgroups of an almost completely decomposable group. In this dissertation we show an extended version of the theorem of Bezout, give a new criterion for the tightness of a completely decomposable subgroup, derive some conditions under which a tight subgroup is regulating and generalize a theorem of Campagna. We give an example of an almost completely decomposable group, all of whose regulating subgroups do not have a quotient with minimal exponent. We show that among the types of elements of a coset modulo a completely decomposable group there exists a unique maximal type and define this type to be -the- coset type. We give criteria for tightness and regulating in term of coset types as well as a representation of the type subgroups using coset types. We introduce the notion of reducible cosets and show their key role for transitions from one completely decomposable subgroup up to another one containing the first one as a proper subgroup. We give an example of a tight, but not regulating subgroup which contains the regulator. We develop the notion of a fully single covered subset of a lattice, show that V-free implies fully single covered, but not necessarily vice versa, and we define an equivalence relation on the set of all finite subsets of a given lattice. We develop some extension of ordinary Hasse diagrams, and apply the lattice theoretic results on the lattice of types and almost completely decomposable groups.
Priority task of the thesis was to replace oxygen atoms in sulfur oxoanions SOnm– or imido groups in sulfur polyimido anions S(NR)nm– isoelectronically by R2C-methylene groups. This would open a wide avenue to new target molecules containing a formally double bonded carbon next to formally double bonded nitrogen atoms in highly charged sulfur-centred anions like S(CR2)x(NR)ym–. They clearly are reminiscent to sulfur ylides. Both, alkylendiimidosulfites and alkylentriimidosulfates are accessible via deprotonaton of the corresponding alkyldiimidosulfinates and alkyltriimidosulfonates with methyllithium. The reactivity of the novel compounds is dominated by the carbanionic centre. Addition reactions to another SN formal doubble bond are feasible and are leading to the yet unknown imidoanalogues compounds alkyl-bis-(diimidosulfinates) and alkyl-bis-(triimidosulfonates).
Implications of Advanced Glycation Endproducts in Oxidative Stress and Neurodegenerative Disorders
(2001)
The reactions of reducing sugars with primary amino groups are the most common nonenzymatic modifications of proteins. Subsequent rearrangements, oxidations, and dehydrations yield a heterogeneous group of mostly colored and fluorescent compounds, termed "Maillard products" or advanced glycation end products (AGEs). AGE formation has been observed on long-lived proteins such as collagen, eye lens crystalline, and in pathological protein deposits in Alzheimer's (AD) and Parkinson's disease (PD) and dialysis-related amyloidosis. AGE-modified proteins are also involved in the complications of diabetes. AGEs accumulate in the the ß-amyloid plaques and neurofibrillary tangles (NFT) associated with AD and in the Lewy bodies characteristic of PD. Increasing evidence supports a role for oxidative stress in neurodegenerative disorders such as AD and PD. AGEs have been shown to contribute towards oxidative damage and chronic inflammation, whereby activated microglia secrete cytokines and free radicals, including nitric oxide (NO). Roles proposed for NO in the pathophysiology of the central nervous system are increasingly diverse and range from intercellular signaling, through necrosis of cells and invading pathogens, to the involvement of NO in apoptosis. Using in vitro experiments, it was shown that AGE-modified bovine serum albumin (BSA-AGE) and AGE-modified ß-amyloid, but not their unmodified proteins, induce NO production in N-11 murine microglia cells. This was mediated by the receptor for AGEs (RAGE) and upregulation of the inducible nitric oxide synthase (iNOS). AGE-induced enzyme activation and NO production could be blocked by intracellular-acting antioxidants: Ginkgo biloba special extract EGb 761, the estrogen derivative, 17ß-estradiol, R-(+)-thioctic acid, and a nitrone-based free radical trap, N-tert.-butyl-*-phenylnitrone (PBN). Methylglyoxal (MG) and 3-deoxyglucosone (3-DG), common precursors in the Maillard reaction, were also tested for their ability to induce the production of NO in N-11 microglia. However, no significant changes in nitrite levels were detected in the cell culture medium. The significance of these findings was supported by in vivo immunostaining of AD brains. Single and double immunostaining of cryostat sections of normal aged and AD brains was performed with polyclonal antibodies to AGEs and iNOS and monoclonal antibodies to Aß and PHF-1 (marker for NFT) and reactive microglia. In aged normal individuals as well as early stage AD brains (i.e. no pathological findings in isocortical areas), a few astrocytes showed co-localisation of AGE and iNOS in the upper neuronal layers of the temporal (Area 22) and entorhinal (Area 28, 34) cortices compared with no astrocytes detected in young controls. In late AD brains, there was a much denser accumulation of astrocytes co-localised with AGE and iNOS in the deeper and particularly upper neuronal layers. Also, numerous neurons with diffuse AGE but not iNOS reactivity and some AGE and iNOS-positive microglia were demonstrated, compared with only a few AGE-reactive neurons and no microglia in controls. Finally, astrocytes co-localised with AGE and iNOS as well as AGE and ß-amyloid were found surrounding mature but not diffuse ß-amyloid plaques in the AD brain. Parts of NFT were AGE-immunoreactive. Immunohistochemical staining of cryostat sections of normal aged and PD brains was performed with polyclonal antibodies to AGEs. The sections were counterstained with monoclonal antibodies to neurofilament components and a-synuclein. AGEs and a-synuclein were colocalized in very early Lewy bodies in the substantia nigra of cases with incidental Lewy body disease. These results support an AGE-induced oxidative damage due to the action of free radicals, such as NO, occurring in the AD and PD brains. Furthermore, the involvement of astrocytes and microglia in this pathological process was confirmed immunohistochemically in the AD brain. It is suggested that oxidative stress and AGEs participate in the very early steps of Lewy body formation and resulting cell death in PD. Since the iNOS gene can be regulated by redox-sensitive transcription factors, the use of membrane permeable antioxidants could be a promising strategy for the treatment and prevention of chronic inflammation in neurodegenerative disorders.
This study has focused on hydrogeological and hydrochemical settings of the Northern Namibian Kalahari Catchment which is the Namibian part of the Makgadikgadi-Kalahari-Catchment. Recharge has been the subject of process-understanding, quantification and regionalisation. Within the semiarid study area a bimodal surface constitution is prominent: hardrocks areas allow for fast infiltration along karsts and joints, whereas areas covered by unconsolidated sediments receive minor diffuse recharge and locally some preferred flow path recharge develops along shrinkage cracks and rootlets. Five substratum classes have been soil physically studied: Pans and vleis, brown to red soils, dune sand, soil with an aeolian influence, and calcrete. Aeolian sands are most promising for the development of direct diffuse recharge. Recharge by preferred flow might occur in all soil classes either due to joints in calcrete or structures and rootlets in soils. All soil classes contribute to indirect recharge because even the dune sand allows, albeit very locally, the generation of runoff. The occurrences of recharge through the unconsolidated soil and the hardrocks have been confirmed by hydrograph interpretation and by a study of hydrochemical data which identified groundwater of flood water and flood water after soil passage composition. Other prominent hydrochemical processes in the Kalahari are associated with the carbonate-equilibrium-system, mixing with highly mineralised water that is either sulphate (central area) or chloride dominated (fringe area) and development of sodium hydrogencarbonate water types. The latter is mostly generated by feldspar weathering. Variations of the hydrochemical compositions were observed for shallow groundwaters. They do not only reflect the recharge amount but also the recharge conditions, e.g. a wetter year is allowing more vegetation which increases the hydrogencarbonate content. Inverse determination of recharge by the chloride mass balance method gives recharge amounts between 0.2 and locally more than 100 mm/a. The least favoured recharge conditions are found for Kalahari covered areas, the largest amount occurs in the Otavi area. The distribution of recharge areas within the catchment is rather complex and regionalisation of recharge for the entire catchment was done by a forward approach using satellite images and by an inverse approach using hydrochemical data. From the inverse hydrochemical approach a basin-wide balanced recharge amount of 1.39 mm/a is achieved. The forward approach gave a basin-wide figure of 0.88 (minimum assumption) to 4.53 mm/a (maximum assumption). A simplistic groundwater flow model confirmed the results from the minimum recharge regionalisation by satellite images and the result from the hydrochemical approach. Altogether a mutually verified basin-wide recharge figure of ca. 1 mm/a turns out.
The social organization of insect colonies has long fascinated naturalists. One of the main features of colony organization is division of labor, whereby each member of the colony specializes in a subset of all tasks required for successful group functioning. The most striking aspect of division of labor is its plasticity: workers switch between tasks in response to external challenges and internal perturbations. The mechanisms underlying flexible division of labor are far from being understood. In order to comprehend how the behavior of individuals gives rise to flexible collective behavior, several questions need to be addressed: We need to know how individuals acquire information about their colony's current demand situation; how they then adjust their behavior according; and which mechanisms integrate dozens or thousands of insect into a higher-order unit. With these questions in mind I have examined two examples of collective and flexible behavior in social bees. First, I addressed the question how a honey bee colony controls its pollen collection. Pollen foraging in honey bees is precisely organized and carefully regulated according to the colony's needs. How this is achieved is unclear. I investigated how foragers acquire information about their colony's pollen need and how they then adjust their behavior. A detailed documentation of pollen foragers in the hive under different pollen need conditions revealed that individual foragers modulate their in-hive working tempo according to the actual pollen need of the colony: Pollen foragers slowed down and stayed in the hive longer when pollen need was low and spent less time in the hive between foraging trips when pollen need of their colony was high. The number of cells inspected before foragers unloaded their pollen load did not change and thus presumably did not serve as cue to pollen need. In contrast, the trophallactic experience of pollen foragers changed with pollen need conditions: trophallactic contacts were shorter when pollen need was high and the number and probability of having short trophallactic contacts increased when pollen need increased. Thus, my results have provided support for the hypothesis that trophallactic experience is one of the various information pathways used by pollen foragers to assess their colony's pollen need. The second example of collective behavior I have examined in this thesis is the control of nest climate in bumble bee colonies, a system differing from pollen collection in honey bees in that information about task need (nest climate parameters) is directly available to all workers. I have shown that an increase in CO2 concentration and temperature level elicits a fanning response whereas an increase in relative humidity does not. The fanning response to temperature and CO2 was graded; the number of fanning bees increased with stimulus intensity. Thus, my study has evidenced flexible colony level control of temperature and CO2. Further, I have shown that the proportion of total work force a colony invests into nest ventilation does not change with colony size. However, the dynamic of the colony response changes: larger colonies show a faster response to perturbations of their colony environment than smaller colonies. Thus, my study has revealed a size-dependent change in the flexible colony behavior underlying homeostasis. I have shown that the colony response to perturbations in nest climate is constituted by workers who differ in responsiveness. Following a brief review of current ideas and models of self-organization and response thresholds in insect colonies, I have presented the first detailed investigation of interindividual variability in the responsiveness of all workers involved in a collective behavior. My study has revealed that bumble bee workers evidence consistent responses to certain stimulus levels and differ in their response thresholds. Some consistently respond to low stimulus intensities, others consistently respond to high stimulus intensities. Workers are stimulus specialists rather than task specialists. Further, I have demonstrated that workers of a colony differ in two other parameters of responsiveness: response probability and fanning activity. Response threshold, response probability and fanning activity are independent parameters of individual behavior. Besides demonstrating and quantifying interindividual variability, my study has provided empirical support for the idea of specialization through reinforcement. Response thresholds of fanning bees decreased over successive trials. I have discussed the importance of interindividual variability for specialization and the collective control of nest climate and present a general discussion of self-organization and selection. This study contributes to our understanding of individual behavior and collective structure in social insects. A fascinating picture of social organization is beginning to emerge. In place of centralized systems of communication and information transmission, insect societies frequently employ mechanisms based upon self-organization. Self-organization promises to be an important and unifying principle in physical, chemical and biological systems.
For many active volcanoes all over the world a civil protection program, normally combined with hazard maps, exists. Optimising of hazard maps and the associated hazard assessment implies a detailed knowledge of the volcanostratigraphy, because the deposits provoke information on the potential behaviour during a new activity cycle. Pyroclastic deposits, however, may vary widely in thickness and distribution over very short lateral distances. High resolution characterisation of single strata often cannot be archived, if solely sedimentological and geochemical methods are used. Gamma-ray measurements taken in the field combined with grain-size depended magnetic susceptibility measurements made in the laboratory are used in this work to optimise the resolution of volcanostratigraphic investigations. The island of Vulcano is part of the Aeolian Archipelago sited of the northern coast of Sicily. La Fossa cone is the active centre of Vulcano, where fumarolic and seismic activity can be observed. The cone was built up during the last 6,000 years, whereby the last eruption period is dated to historic times (1888-1890). For the tuff cone La Fossa the most likely volcanic hazards are the emplacement of pyroclastic deposits as well as gas hazards (especially SOx and CO2), due to this the detailed knowledge of the stratigraphy is mandatory. Most of the population resides in Vulcano Porto and the nearby sited peninsula of Vulcanello, which are highly endangered locations for a future eruption scenario. Measurements, made in standard outcrops, allow a characterisation of the successions Punte Nere, Tufi Varicolori, Palizzi, Commenda, and Cratere Attuale. A discrimination of all successions by solely one of the methods is rarely possible. In some cases, however, the combination of the methods leads to clear results. It can also be noticed that the exposition as well as the sedimentation type (wet-surge or dry-surge deposits) affect the measurements. In general it can be assumed that the higher the magma is evolved the higher the g -ray values and the lower the susceptibility values. Measurements from the Wingertsberg (Laacher See deposits, Eifel, W-Germany) show clearly that a higher degree of magma evolution correlates with lower susceptibility and higher gamma-ray values. Variations of the values can be observed not only by the change of the degree of magmatic evolution but also by the inhomogeneous deposition conditions. Particularly the gamma-ray measurements show lower values for the wet-surge deposits than for the dry-surge deposits, even though the erupted material has the same geochemical composition. This can be explained especially by reactions inside of the moist eruption cloud and short-time after deposition, when easily soluble elements like K, U, and Th can be leached by these aggressive fluids. Even extended exposition and high water content can provoke depletion of various elements within the complete or parts of the outcrop, too. If the deposits are affected by a fumarolic activity especially the susceptibility values show significant variations, whereas in general extreme low values are observed. Contamination of deposits also can occur, if they are overlain by weathered deposits of higher concentration of K, U, and Th. Weathering and mobilisation within the upper deposits can generate an element enrichment within the lower deposits. In general the element ratios of the barried underlying deposits are less affected than the exposed ones. After gauging the values of the well defined succession for standard outcrops undefined outcrops were measured. These outcrops are not clearly classified by sedimentological and geochemical methods, thus a correlation with the combined geophysical methods is useful. In general the combination of the methods allows a correlation, although in some cases more than one interpretation is possible. But in connection with time marker horizons as well as sedimentological features an interpretation is feasible. These situations show that a classification solely based on geophysical methods is possible for many cases but, if the volcanic system is more complex, a combination with sedimentological and geochemical methods may be needed. The investigations on Vulcano, documented in this work, recommend a re-interpretation of the dispersial of some successions of La Fossa cone, especially the presumption that Tufi Varicolori only exist inside of the Caldera of La Fossa. As a consequence the eruption and energy model especially for Tufi Varicolori have to be reviewed.