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We present an application of imprecise probability theory to the quantification of uncertainty in the integrated assessment of climate change. Our work is motivated by the fact that uncertainty about climate change is pervasive, and therefore requires a thorough treatment in the integrated assessment process. Classical probability theory faces some severe difficulties in this respect, since it cannot capture very poor states of information in a satisfactory manner. A more general framework is provided by imprecise probability theory, which offers a similarly firm evidential and behavioural foundation, while at the same time allowing to capture more diverse states of information. An imprecise probability describes the information in terms of lower and upper bounds on probability. For the purpose of our imprecise probability analysis, we construct a diffusion ocean energy balance climate model that parameterises the global mean temperature response to secular trends in the radiative forcing in terms of climate sensitivity and effective vertical ocean heat diffusivity. We compare the model behaviour to the 20th century temperature record in order to derive a likelihood function for these two parameters and the forcing strength of anthropogenic sulphate aerosols. Results show a strong positive correlation between climate sensitivity and ocean heat diffusivity, and between climate sensitivity and absolute strength of the sulphate forcing. We identify two suitable imprecise probability classes for an efficient representation of the uncertainty about the climate model parameters and provide an algorithm to construct a belief function for the prior parameter uncertainty from a set of probability constraints that can be deduced from the literature or observational data. For the purpose of updating the prior with the likelihood function, we establish a methodological framework that allows us to perform the updating procedure efficiently for two different updating rules: Dempster's rule of conditioning and the Generalised Bayes' rule. Dempster's rule yields a posterior belief function in good qualitative agreement with previous studies that tried to constrain climate sensitivity and sulphate aerosol cooling. In contrast, we are not able to produce meaningful imprecise posterior probability bounds from the application of the Generalised Bayes' Rule. We can attribute this result mainly to our choice of representing the prior uncertainty by a belief function. We project the Dempster-updated belief function for the climate model parameters onto estimates of future global mean temperature change under several emissions scenarios for the 21st century, and several long-term stabilisation policies. Within the limitations of our analysis we find that it requires a stringent stabilisation level of around 450 ppm carbon dioxide equivalent concentration to obtain a non-negligible lower probability of limiting the warming to 2 degrees Celsius. We discuss several frameworks of decision-making under ambiguity and show that they can lead to a variety of, possibly imprecise, climate policy recommendations. We find, however, that poor states of information do not necessarily impede a useful policy advice. We conclude that imprecise probabilities constitute indeed a promising candidate for the adequate treatment of uncertainty in the integrated assessment of climate change. We have constructed prior belief functions that allow much weaker assumptions on the prior state of information than a prior probability would require and, nevertheless, can be propagated through the entire assessment process. As a caveat, the updating issue needs further investigation. Belief functions constitute only a sensible choice for the prior uncertainty representation if more restrictive updating rules than the Generalised Bayes'Rule are available.
Adhesion of biological cells to their environment is mediated by two-dimensional clusters of specific adhesion molecules which are assembled in the plasma membrane of the cells. Due to the activity of the cells or external influences, these adhesion sites are usually subject to physical forces. In recent years, the influence of such forces on the stability of cellular adhesion clusters was increasingly investigated. In particular, experimental methods that were originally designed for the investigation of single bond rupture under force have been applied to investigate the rupture of adhesion clusters. The transition from single to multiple bonds, however, is not trivial and requires theoretical modelling. Rupture of biological adhesion molecules is a thermally activated, stochastic process. In this work, a stochastic model for the rupture and rebinding dynamics of clusters of parallel adhesion molecules under force is presented. In particular, the influence of (i) a constant force as it may be assumed for cellular adhesion clusters is investigated and (ii) the influence of a linearly increasing force as commonly used in experiments is considered. Special attention is paid to the force-mediated cooperativity of parallel adhesion bonds. Finally, the influence of a finite distance between receptors and ligands on the binding dynamics is investigated. Thereby, the distance can be bridged by polymeric linker molecules which tether the ligands to a substrate.
This paper focuses on mysteries written by the Afro-American women authors Barbara Neely and Valerie Wilson Wesley. Both authors place a black woman in the role of the detective - an innovative feature not only in the realm of female detective literature of the past two decades but also with regard to the current discourse about race and class in US-American society. This discourse is important because detective novels are considered popular literature and thus a mass product designed to favor commercial instead of literary claims. Thus, the focus is placed on the development of the two protagonists, on their lives as detectives and as black women, in order to find out whether or not and how the genre influences the depiction of Afro-American experiences. It appears that both of these detective series represent Afro-American culture in different ways, which confirms a heterogenic development of this ethnic group. However, the protagonist's search for identity and their relationships to white people could be identified as a major unifying claim of Afro-American literature. With differing intensity, the authors Neely and Wesley provide the white or mainstream reader with insight into their culture and confront the reader's ignorance of black culture. In light of this, it is a great achievement that Neely and Wesley have reached not only a black audience but also a growing number of white readers.
Nitrogen is an essential macronutrient for plants and nitrogen fertilizers are indispensable for modern agriculture. Unfortunately, we know too little about how plants regulate their use of soil nitrogen, to maximize fertilizers-N use by crops and pastures. This project took a dual approach, involving forward and reverse genetics, to identify N-regulators in plants, which may prove useful in the future to improve nitrogen-use efficiency in agriculture. To identify nitrogen-regulated transcription factor genes in Arabidopsis that may control N-use efficiency we developed a unique resource for qRT-PCR measurements on all Arabidpsis transcription factor genes. Using closely spaced, gene-specific primer pairs and SYBR® Green to monitor amplification of double-stranded DNA, transcript levels of 83% of all target genes could be measured in roots or shoots of young Arabidopsis wild-type plants. Only 4% of reactions produced non-specific PCR products, and 13% of TF transcripts were undetectable in these organs. Measurements of transcript abundance were quantitative over six orders of magnitude, with a detection limit equivalent to one transcript molecule in 1000 cells. Transcript levels for different TF genes ranged between 0.001-100 copies per cell. Real-time RT-PCR revealed 26 root-specific and 39 shoot-specific TF genes, most of which have not been identified as organ-specific previously. An enlarged and improved version of the TF qRT-PCR platform contains now primer pairs for 2256 Arabidopsis TF genes, representing 53 gene families and sub-families arrayed on six 384-well plates. Set-up of real-time PCR reactions is now fully robotized. One researcher is able to measure expression of all 2256 TF genes in a single biological sample in a just one working day. The Arabidopsis qRT-PCT platform was successfully used to identify 37 TF genes which transcriptionaly responded at the transcriptional level to N-deprivation or to nitrate per se. Most of these genes have not been characterized previously. Further selection of TF genes based on the responses of selected candidates to other macronutrients and abiotic stresses allowed to distinguish between TFs regulated (i) specifically by nitrogen (29 genes) (ii) regulated by general macronutrient or by salt and osmotic stress (6 genes), and (iii) responding to all major macronutrients and to abiotic stresses. Most of the N-regulated TF genes were also regulated by carbon. Further characterization of sixteen selected TF genes, revealed: (i) lack of transcriptional response to organic nitrogen, (ii) two major types of kinetics of induction by nitrate, (iii) specific responses for the majority of the genes to nitrate but not downstream products of nitrate assimilation. All sixteen TF genes were cloned into binary vectors for constitutive and ethanol inducible over expression, and the first generation of transgenic plants were obtained for almost all of them. Some of the plants constitutively over expressing TF genes under control of the 35S promoter revealed visible phenotypes in T1 generation. Homozygous T-DNA knock out lines were also obtained for many of the candidate TF genes. So far, one knock out line revealed a visible phenotype: retardation of flowering time. A forward genetic approach using an Arabidopsis ATNRT2.1 promoter : Luciferase reporter line, resulted in identification of eleven EMS mutant reporter lines affected in induction of ATNRT2.1 expression by nitrate. These lines could by divided in the following classes according to expression of other genes involved in primary nitrogen and carbon metabolism: (i) lines affected exclusively in nitrate transport, (ii) those affected in nitrate transport, acquisition, but also in glycolysis and oxidative pentose pathway, (iii) mutants affected moderately in nitrate transport, oxidative pentose pathway and glycolysis but not in primary nitrate assimilation. Thus, several different N-regulatory genes may have been mutated in this set of mutants. Map-based cloning has begun to identify the genes affected in these mutants.
In this thesis, we give two constructions for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an L2-metric on Yang-Mills moduli spaces as given by Groisser and Parker. To construct a Riemannian metric on the total space of the Seiberg-Witten bundle in a similar way, we define the reduced gauge group as a subgroup of the gauge group. We show, that the quotient of the premoduli space by the reduced gauge group is isomorphic as a U(1)-bundle to the quotient of the premoduli space by the based gauge group. The total space of this new representation of the Seiberg-Witten bundle carries a natural quotient L2-metric, and the bundle projection is a Riemannian submersion with respect to these metrics. We compute explicit formulae for the sectional curvature of the moduli space in terms of Green operators of the elliptic complex associated with a monopole. Further, we construct a Riemannian metric on the cobordism between moduli spaces for different perturbations. The second construction of a Riemannian metric on the moduli space uses a canonical global gauge fixing, which represents the total space of the Seiberg-Witten bundle as a finite dimensional submanifold of the configuration space. We consider the Seiberg-Witten moduli space on a simply connected Käuhler surface. We show that the moduli space (when nonempty) is a complex projective space, if the perturbation does not admit reducible monpoles, and that the moduli space consists of a single point otherwise. The Seiberg-Witten bundle can then be identified with the Hopf fibration. On the complex projective plane with a special Spin-C structure, our Riemannian metrics on the moduli space are Fubini-Study metrics. Correspondingly, the metrics on the total space of the Seiberg-Witten bundle are Berger metrics. We show that the diameter of the moduli space shrinks to 0 when the perturbation approaches the wall of reducible perturbations. Finally we show, that the quotient L2-metric on the Seiberg-Witten moduli space on a Kähler surface is a Kähler metric.
Diagenetic studies of carbonate rocks focused for a long time on photozoan carbonate assemblages deposited in tropical climates. The results of these investigations were taken as models for the diagenetic evolution of many fossil carbonates. Only in recent years the importance of heterozoan carbonates, generally formed out of the tropics or in deeper waters, was realized. Diagenetic studies focusing on this kind of rocks are still scarce, but indicate that the diagenetic evolution of these rocks might be a better model for many fossil carbonate settings ("calcite-sea" carbonates) than the photozoan model used before. This study deals with the determination of the diagenetic pathways and environments in such shallow-water heterozoan carbonate assemblages. Special emphasis is put on the identification of early, near-seafloor diagenetic processes and on the evaluation of the amount of constructive diagenesis in form of cementation in this diagenetic environment. As study area the Central Mediterranean, the Maltese Islands and Sicily, was chosen. Here two sections were logged in Olio-Miocene shallow-water carbonates consisting of different kinds of heterozoan assemblages. The study area is very suitable for the investigation of constructive early diagenetic processes, as the rocks were never deeply buried and burial diagenetic pressure solution and cementation as cause of lithification could be ruled out. Nevertheless, the carbonate rocks are well lithified and form steep cliffs, implying cementation/lithification in another, shallower diagenetic environment. To determine the diagenetic pathways and environments, detailed transmitted light and cathodoluminescence petrography was carried out on thin sections. Furthermore the stable isotope (δ<sup>18O and δ<sup>13C) composition of the bulk rock, single biota and single cement phases was determined, as well as the major and trace element composition of the single cement phases. Petrographically three (Sicily) to four (Maltese Islands) cementation phases, two phases of fabric selective and one of non-fabric selective dissolution, one phase of neomorphism and one of chemical compaction could be distinguished. The stable isotope measurements of the single cement phases pointed to cement precipitation from marine, marine-derived and meteoric waters. The trace element analysis indicated precipitation under reducing conditions, (A) in an open system with low rock-water interaction on the Maltese Islands and (B) in a closed system with high rock-water interaction on Sicily. For the closed systems case, aragonite as cement source could be concluded because its chemical composition was preserved in the newly formed cements. By integrating these results, diagenetic pathways and environments for the investigated locations were established, and the cement source(s) in the different environments were determined. The diagenetic evolution started in the marine environment with the precipitation of fibrous/fibrous-bladed and epitaxial cement I. These cements formed as High Mg Calcite (HMC) directly out of marine waters. The paleoenvironmentally shallowest part of the section on the Maltese Islands was also exposed to meteoric diagenetic fluids. This meteoric influence lead to the dissolution of aragonitic and HMC skeletons, which sourced the cementation by Low Mg Calcitic (LMC) epitaxial cement II in this part of the Maltese section. Entering the burial-marine environment the main part of dissolution, cementation and neomorphism started to take place. The elevated CO2 content in this environment, caused by the decay of organic matter, lead to the dissolution of aragonitic skeletons, which sourced the cementation by LMC epitaxial cement II, bladed and blocky cements. The earlier precipitated HMC cement phases were either partly dissolved (epitaxial cement I) or neomorphosed to LMC (fibrous/fibrous-bladed and epitaxial cement I). In the burial environment weak chemical compaction took place without sourcing significant amounts of cementation. In a last phase the rocks entered the meteoric realm by uplift, which caused non-fabric selective dissolution. This study shows that early diagenetic processes, taking place at or just below the sediment-water-interface, are very important for the mineralogical stabilization of heterozoan carbonate strata. The main amount of constructive diagenesis in form of cementation takes place in this environment, sourced by dissolution of aragonitic and, to a lesser degree, of HMC skeletons. The results of this study imply that the primary amount of aragonitic skeletons in heterozoan carbonate sediments must be carefully assessed, as they are the main early diagenetic cement source. In fossil heterozoan carbonate rocks, aragonitic skeletons might be the cement source even when no relict structures like micritic envelops or biomolds are preserved. In general, the diagenetic evolution of heterozoan carbonate rocks is a good model for the diagenesis of "calcite-sea" time carbonate rocks.
Stochastic information, to be understood as "information gained by the application of stochastic methods", is proposed as a tool in the assessment of changes in climate. This thesis aims at demonstrating that stochastic information can improve the consideration and reduction of uncertainty in the assessment of changes in climate. The thesis consists of three parts. In part one, an indicator is developed that allows the determination of the proximity to a critical threshold. In part two, the tolerable windows approach (TWA) is extended to a probabilistic TWA. In part three, an integrated assessment of changes in flooding probability due to climate change is conducted within the TWA. The thermohaline circulation (THC) is a circulation system in the North Atlantic, where the circulation may break down in a saddle-node bifurcation under the influence of climate change. Due to uncertainty in ocean models, it is currently very difficult to determine the distance of the THC to the bifurcation point. We propose a new indicator to determine the system's proximity to the bifurcation point by considering the THC as a stochastic system and using the information contained in the fluctuations of the circulation around the mean state. As the system is moved closer to the bifurcation point, the power spectrum of the overturning becomes "redder", i.e. more energy is contained in the low frequencies. Since the spectral changes are a generic property of the saddle-node bifurcation, the method is not limited to the THC, but it could also be applicable to other systems, e.g. transitions in ecosystems. In part two, a probabilistic extension to the tolerable windows approach (TWA) is developed. In the TWA, the aim is to determine the complete set of emission strategies that are compatible with so-called guardrails. Guardrails are limits to impacts of climate change or to climate change itself. Therefore, the TWA determines the "maneuvering space" humanity has, if certain impacts of climate change are to be avoided. Due to uncertainty it is not possible to definitely exclude the impacts of climate change considered, but there will always be a certain probability of violating a guardrail. Therefore the TWA is extended to a probabilistic TWA that is able to consider "probabilistic uncertainty", i.e. uncertainty that can be expressed as a probability distribution or uncertainty that arises through natural variability. As a first application, temperature guardrails are imposed, and the dependence of emission reduction strategies on probability distributions for climate sensitivities is investigated. The analysis suggests that it will be difficult to observe a temperature guardrail of 2°C with high probabilities of actually meeting the target. In part three, an integrated assessment of changes in flooding probability due to climate change is conducted. A simple hydrological model is presented, as well as a downscaling scheme that allows the reconstruction of the spatio-temporal natural variability of temperature and precipitation. These are used to determine a probabilistic climate impact response function (CIRF), a function that allows the assessment of changes in probability of certain flood events under conditions of a changed climate. The assessment of changes in flooding probability is conducted in 83 major river basins. Not all floods can be considered: Events that either happen very fast, or affect only a very small area can not be considered, but large-scale flooding due to strong longer-lasting precipitation events can be considered. Finally, the probabilistic CIRFs obtained are used to determine emission corridors, where the guardrail is a limit to the fraction of world population that is affected by a predefined shift in probability of the 50-year flood event. This latter analysis has two main results. The uncertainty about regional changes in climate is still very high, and even small amounts of further climate change may lead to large changes in flooding probability in some river systems.
The multidrug and toxic compounds extrusion (MATE) family includes hundreds of functionally uncharacterised proteins from bacteria and all eukaryotic kingdoms except the animal kingdom, that function as drug/toxin::Na<sup>+ or H<sup>+ antiporters. In Arabidopsis thaliana the MATE family comprises 56 members, one of which is NIC2 (Novel Ion Carrier 2). Using heterologous expression systems including Escherichia coli and Saccharomyces cerevisiae, and the homologous expression system of Arabidopsis thaliana, the functional characterisation of NIC2 was performed. It has been demonstrated that NIC2 confers resistance of E. coli towards the chemically diverse compounds such as tetraethylammonium chloride (TEACl), tetramethylammonium chloride (TMACl) and a toxic analogue of indole-3-acetic acid, 5-fluoro-indole-acetic acid (F-IAA). Therefore, NIC2 may be able to transport a broad range of drug and toxic compounds. In wild-type yeast the expression of NIC2 increased the tolerance towards lithium and sodium, but not towards potassium and calcium. In A. thaliana, the overexpression of NIC2 led to strong phenotypic changes. Under normal growth condtions overexpression caused an extremely bushy phenotype with no apical dominance but an enhanced number of lateral flowering shoots. The amount of rossette leaves and flowers with accompanying siliques were also much higher than in wild-type plants and the senescence occurred earlier in the transgenic plants. In contrast, RNA interference (RNAi) used to silence NIC2 expression, induced early flower stalk development and flowering compared with wild-type plants. In additon, the main flower stalks were not able to grow vertically, but instead had a strong tendency to bend towards the ground. While NIC2 RNAi seedlings produced many lateral roots outgrowing from the primary root and the root-shoot junction, NIC2 overexpression seedlings displayed longer primary roots that were characterised by a 2 to 4 h delay in the gravitropic response. In addition, these lines exhibited an enhanced resistance to exogenously applied auxins, i.e. indole-3-acetic acid (IAA) and indole-3-butyric acid (IBA) when compared with the wild-type roots. Based on these results, it is suggested that the NIC2 overexpression and NIC2 RNAi phenotypes were due to decreased or increased levels of auxin, respectively. The ProNIC2:GUS fusion gene revealed that NIC2 is expressed in the stele of the elongation zone, in the lateral root cap, in new lateral root primordia, and in pericycle cells of the root system. In the vascular tissue of rosette leaves and inflorescence stems, the expression was observed in the xylem parenchyma cells, while in siliques it was also in vascular tissue, but as well in the dehiscence and abscission zones. The organ- and tissue-specific expression sites of NIC2 correlate with the sites of auxin action in mature Arabidopsis plants. Further experiments using ProNIC2:GUS indicated that NIC2 is an auxin-inducible gene. Additionally, during the gravitropic response when an endogenous auxin gradient across the root tip forms, the GUS activity pattern of the ProNIC2:GUS fusion gene markedly changed at the upper side of the root tip, while at the lower side stayed unchanged. Finally, at the subcellular level NIC2-GFP fusion protein localised in the peroxisomes of Nicotana tabacum BY2 protoplasts. Considering the experimental results, it is proposed that the hypothetical function of NIC2 is the efflux transport which takes part in the auxin homeostasis in plant tissues probably by removing auxin conjugates from the cytoplasm into peroxisomes.
The protection of species is one major focus in conservation biology. The basis for any management concept is the knowledge of the species autecology. In my thesis, I studied the life-history traits and population dynamics of the endangered Lesser Spotted Woodpecker (Picoides minor) in Central Europe. Here, I combine a range of approaches, from empirical investigations of a Lesser Spotted Woodpecker population in the Taunus low mountain range in Germany, the analysis of empirical data and the development of an individual-based stochastic model simulating the population dynamics. In the field studies I collected basic demographic data of reproductive success and mortality. Moreover, breeding biology and behaviour were investigated in detail. My results showed a significant decrease of the reproductive success with later timing of breeding, caused by deterioration in food supply. Moreover, mate fidelity was of benefit, since pairs composed of individuals that bred together the previous year started earlier with egg laying and obtained a higher reproductive success. Both sexes were involved in parental care, but the care was only shared equally during incubation and the early nestling stage. In the late nestling stage, parental care strategies differed between sexes: Females considerably decreased feeding rate with number of nestlings and even completely deserted small broods. Males fed their nestlings irrespective of brood size and compensated for the females absence. The organisation of parental care in the Lesser Spotted Woodpecker is discussed to provide the possibility for females to mate with two males with separate nests and indeed, polyandry was confirmed. To investigate the influence of the observed flexibility in the social mating system on the population persistence, a stochastic individual-based model simulating the population dynamics of the Lesser Spotted Woodpecker was developed, based on empirical results. However, pre-breeding survival rates could not be obtained empirically and I present in this thesis a pattern-oriented modelling approach to estimate pre-breeding survival rates by comparing simulation results with empirical pattern of population structure and reproductive success on population level. Here, I estimated the pre-breeding survival for two Lesser Spotted Woodpecker populations on different latitudes to test the reliability of the results. Finally, I used the same simulation model to investigate the effect of flexibility in the mating system on the persistence of the population. With increasing rate of polyandry in the population, the persistence increased and even low rates of polyandry had a strong influence. Even when presuming only a low polyandry rate and costs of polyandry in terms of higher mortality and lower reproductive success for the secondary male, the positive effect of polyandry on the persistence of the population was still strong. This thesis greatly helped to increase the knowledge of the autecology of an endangered woodpecker species. Beyond the relevance for the species, I could demonstrate here that in general flexibility in mating systems are buffer mechanisms and reduce the impact of environmental and demographic noise.
Origin and symmetry of the observed global magnetic fields in galaxies are not fully understood. We intend to clarify the question of the magnetic field origin and investigate the global action of the magneto-rotational instability (MRI) in galactic disks with the help of 3D global magneto-hydrodynamical (MHD) simulations. The calculations were done with the time-stepping ZEUS 3D code using massive parallelization. The alpha-Omega dynamo is known to be one of the most efficient mechanisms to reproduce the observed global galactic fields. The presence of strong turbulence is a pre-requisite for the alpha-Omega dynamo generation of the regular magnetic fields. The observed magnitude and spatial distribution of turbulence in galaxies present unsolved problems to theoreticians. The MRI is known to be a fast and powerful mechanism to generate MHD turbulence and to amplify magnetic fields. We find that the critical wavelength increases with the increasing of magnetic fields during the simulation, transporting the energy from critical to larger scales. The final structure, if not disrupted by supernovae explosions, is the structure of `thin layers' of thickness of about 100 pcs. An important outcome of all simulations is the magnitude of the horizontal components of the Reynolds and Maxwell stresses. The result is that the MRI-driven turbulence is magnetic-dominated: its magnetic energy exceeds the kinetic energy by a factor of 4. The Reynolds stress is small and less than 1% of the Maxwell stress. The angular momentum transport is thus completely dominated by the magnetic field fluctuations. The volume-averaged pitch angle is always negative with a magnitude of about -30. The non-saturated MRI regime is lasting sufficiently long to fill the time between the galactic encounters, independently of strength and geometry of the initial field. Therefore, we may claim the observed pitch angles can be due to MRI action in the gaseous galactic disks. The MRI is also shown to be a very fast instability with e-folding time proportional to the time of one rotation. Steep rotation curves imply a stronger growth for the magnetic energy due to MRI. The global e-folding time is from 44 Myr to 100 Myr depending on the rotation profile. Therefore, MRI can explain the existence of rather large magnetic field in very young galaxies. We also have reproduced the observed rms values of velocities in the interstellar turbulence as it was observed in NGC 1058. We have shown with the simulations that the averaged velocity dispersion of about 5 km/s is a typical number for the MRI-driven turbulence in galaxies, which agrees with observations. The dispersion increases outside of the disk plane, whereas supernovae-driven turbulence is found to be concentrated within the disk. In our simulations the velocity dispersion increases a few times with the heights. An additional support to the dynamo alpha-effect in the galaxies is the ability of the MRI to produce a mix of quadrupole and dipole symmetries from the purely vertical seed fields, so it also solves the seed-fields problem of the galactic dynamo theory. The interaction of magneto-rotational instability and random supernovae explosions remains an open question. It would be desirable to run the simulation with the supernovae explosions included. They would disrupt the calm ring structure produced by global MRI, may be even to the level when we can no longer blame MRI to be responsible for the turbulence.