Statistical problems related to excitation threshold and reset value of membrane potentials

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für spikende Neuronen ist das Folgende. Zwischen den Spikes verhält sich das Membranpotential wie ein Diffusionsprozess X der durch die SDGL dX_t= beta(X_t) dt+ sigma(X_t) dB_t gegeben ist, wobei (B_t) eine Standard-Brown'sche Bewegung bezeichnet. Spikes erklärt man wie folgt. Sobald das Potential X eine gewisse Exzitationsschwelle S überschreitet entsteht ein Spike. Danach wird das Potential wieder auf einen bestimmten Wert x_0 zurückgesetzt. In Anwendungen ist es manchmal möglich, einen Diffusionsprozess X zwischen den Spikes zu beobachten und die Koeffizienten der SDGL beta() und sigma() zu schätzen. Dennoch ist es nötig, die Schwellen x_0 und S zu bestimmen um das Modell festzulegen. Eine Möglichkeit, dieses Problem anzugehen, ist x_0 und S als Parameter eines statistischen Modells aufzufassen und diese zu schätzen. In der vorliegenden Arbeit werden vier verschiedene Fälle diskutiert, in denen wir jeweils annehmen, dass das Membranpotential X zwischen den Spikes eine Brown'sche Bewegung mit Drift, eine geometrische Brown'sche Bewegung, ein Ornstein-Uhlenbeck Prozess oder ein Cox-Ingersoll-Ross Prozess ist. Darüber hinaus beobachten wir die Zeiten zwischen aufeinander folgenden Spikes, die wir als iid Treffzeiten der Schwelle S von X gestartet in x_0 auffassen. Die ersten beiden Fälle ähneln sich sehr und man kann jeweils den Maximum-Likelihood-Schätzer explizit angeben. Darüber hinaus wird, unter Verwendung der LAN-Theorie, die Optimalität dieser Schätzer gezeigt. In den Fällen OU- und CIR-Prozess wählen wir eine Minimum-Distanz-Methode, die auf dem Vergleich von empirischer und wahrer Laplace-Transformation bezüglich einer Hilbertraumnorm beruht. Wir werden beweisen, dass alle Schätzer stark konsistent und asymptotisch normalverteilt sind. Im letzten Kapitel werden wir die Effizienz der Minimum-Distanz-Schätzer anhand simulierter Daten überprüfen. Ferner, werden Anwendungen auf reale Datensätze und deren Resultate ausführlich diskutiert.

Petrogenesis of dunite, wehrlite and websterite xenoliths from Kimberley, South Africa: Origin as mantle peridotites of cumulates

Dunite, wehrlite and websterite xenoliths occur amongst a large abundance of mantle xenoliths in kimberlites of the Kimberley cluster in South Africa. Up to know they have mostly been neglected. On the basis of texture, major and trace elements, oxygen isotopes as well as Re-Os isotope characteristics, they can be subdivided into two groups. A coarse-grained mantle peridotite group, comprising dunite, wehrlite and websterite xenoliths, that are similar to fertile peridotites and represent upper mantle assemblages that are differently influenced by mantle metasomatism. And a cumulate group, containing fine-grained Fe-rich dunite xenoliths that represent cumulates of flood basalt magmatism related to ~183 Ma Karoo and ~2.7 Ga Ventersdorp events in southern Africa. Dunite, wehrlite and websterite xenoliths have preserved a complex history of melt depletion and metasomatic re-enrichment events, which gives information about the different re-enrichment stages of the subcratonic lithospheric mantle and the spatial differences within the Kaapvaal craton upper mantle. Websterite xenoliths comprise orthopyroxene (40-85 Vol. %), clinopyroxene (5-42 Vol. %), garnet (4-10 Vol. %) and subordinately olivine, while dunite and wehrlite xenoliths contain predominantly olivine (65-100 Vol %) and subordinately orthopyroxene, clinopyroxene and garnet. High melt depletion and a dunitic to harzburgitic protolith composition are reflected by high forsterite (Fo90-92) and high olivine NiO contents (2800-5000 ppm) and high orthopyroxene Mg# (Mg/(Mg+Fe)) of 0.91-0.93. Re-depletion ages of predominantly 2.9 Ga reflect a minimum age of melt depletion. Melt depletion ceased in conjunction with collision of the Kimberley block with the Witwatersrand block ~2.9 Ga ago. Subduction related re-fertilisation of the previously depleted mantle xenoliths is documented by i) amoeboid textured orthopyroxene, clinopyroxene and garnet, which crystallized in schlieren along olivine grain boundaries, ii) high whole-rock SiO2, Al2O3, CaO, TiO2, FeO contents, iii) low oxygen isotope ratios in clinopyroxene and garnet of 4.8-5.4 ‰ and 4.7-5.3 ‰, respectively and iv) trace element compositions of wehrlitic clinopyroxene and garnet in equilibrium with high-pressure partial melts of eclogite. Trace element disequilibrium of orthopyroxene with clinopyroxene and garnet indicates a separate origin for orthopyroxene, on one side as primary mantle orthopyroxene in dunite and wehrlite xenoliths and on the other side as reaction product with Si-rich melts produced by partial melting of eclogite. This reaction triggered replacement of olivine by orthopyroxene in the surrounding mantle and produced the typical Si-rich composition of Kaapvaal mantle peridotites. Partial melting of eclogite at higher temperatures produced a second metasomatic melt with lower SiO2, but higher Al2O3, CaO, FeO, Ti, Zr, Hf and a low oxygen isotope ratio. This melt triggered clinopyroxene and locally garnet and rutile crystallization in percolation veins, replacing olivine and orthopyroxene in the Kaapvaal upper mantle. Additionally, websterite xenoliths have experienced late stage cryptic metasomatism by the host kimberlite melt, changing the trace element composition of clinopyroxene, orthopyroxene and garnet to different extent. Hence websterite and most fertile lherzolite xenoliths have experienced three metasomatic events: i) reaction with high-Si melt, ii) percolation of subduction related silica melt with lower SiO2 content and iii) cryptic metasomatism by kimberlite. In contrast, dunite and wehrlite xenoliths have only experienced the second metasomatic event. They represent mantle lithologies further away from metasomatising agents. The Fe-rich dunites comprise olivine neoblasts with subordinate olivine porphyroclasts and parallel-orientated needles of ilmenite, which may enclose spinel. The lower forsterite and NiO contents of olivine in Fe-rich dunites compared to mantle peridotite xenoliths (Fo87-89 vs. Fo93-95 and 1300-2800ppm vs. 2200-3900 ppm, respectively), rules out a restitic origin. Cr-rich spinels are remnants of the original cumulate mineralogy that survived a late stage metasomatic overprint related to the production of the host kimberlite, producing ilmenite and phlogopite in some samples. Olivine porphyroclasts and neoblasts have different trace element compositions, the latter having high Ti, V, Cr and Ni and low Zn, Zr and Nb contents, indicating contrasting origins for neoblasts and porphyroclasts. The dunites have high 187Os/188Os ratios (0.11-0.15) indicating young (Phanerozoic) model ages for most samples, whereas three samples show isotopic mixtures between Phanerozoic neoblasts and ancient porphyroclastic material. Most Fe-rich dunite xenoliths can be interpreted as cumulates of fractional crystallization of Karoo magmatism, whereas the porphyroclasts are interpreted to be remnants from the much earlier Archaean Ventersdorp magmatism.

Climate change in Libya and desertification of Jifara Plain

The study was arranged to manifest its objectives through preceding it with an intro-duction. Particular attention was paid in the second part to detect the physical settings of the study area, together with an attempt to show the climatic characteristics in Libya. In the third part, observed temporal and spatial climate change in Libya was investigated through the trends of temperature, precipitation, relative humidity and cloud amount over the peri-ods (1946-2000), (1946-1975), and (1976-2000), comparing the results with the global scales. The forth part detected the natural and human causes of climate change concentrat-ing on the greenhouse effect. The potential impacts of climate change on Libya were ex-amined in the fifth chapter. As a case study, desertification of Jifara Plain was studied in the sixth part. In the seventh chapter, projections and mitigations of climate change and desertification were discussed. Ultimately, the main results and recommendations of the study were summarized. In order to carry through the objectives outlined above, the following methods and approaches were used: a simple linear regression analysis was computed to detect the trends of climatic parameters over time; a trend test based on a trend-to-noise-ratio was applied for detecting linear or non-linear trends; the non-parametric Mann-Kendall test for trend was used to reveal the behavior of the trends and their significance; PCA was applied to construct the all-Libya climatic parameters trends; aridity index after Walter-Lieth was shown for computing humid respectively arid months in Libya; correlation coefficient, (after Pearson) for detecting the teleconnection between sun spot numbers, NAOI, SOI, GHGs, and global warming, climate changes in Libya; aridity index, after De Martonne, to elaborate the trends of aridity in Jifara Plain; Geographical Information System and Re-mote Sensing techniques were applied to clarify the illustrations and to monitor desertifi-cation of Jifara Plain using the available satellite images MSS, TM, ETM+ and Shuttle Radar Topography Mission (SRTM). The results are explained by 88 tables, 96 figures and 10 photos. Temporal and spatial temperature changes in Libya indicated remarkably different an-nual and seasonal trends over the long observation period 1946-2000 and the short obser-vation periods 1946-1975 and 1976-2000. Trends of mean annual temperature were posi-tive at all study stations except at one from 1946-2000, negative trends prevailed at most stations from 1946-1975, while strongly positive trends were computed at all study stations from 1976-2000 corresponding with the global warming trend. Positive trends of mean minimum temperatures were observed at all reference stations from 1946-2000 and 1976-2000, while negative trends prevailed at most stations over the period 1946-1975. For mean maximum temperature, positive trends were shown from 1946-2000 and from 1976-2000 at most stations, while most trends were negative from 1946-1975. Minimum tem-peratures increased at nearly more than twice the rate of maximum temperatures at most stations. In respect of seasonal temperature, warming mostly occurred in summer and au-tumn in contrast to the global observations identifying warming mostly in winter and spring in both study periods. Precipitation across Libya is characterized by scanty and sporadically totals, as well as high intensities and very high spatial and temporal variabilities. From 1946-2000, large inter-annual and intra-annual variabilities were observed. Positive trends of annual precipi-tation totals have been observed from 1946-2000, negative trends from 1976-2000 at most stations. Variabilities of seasonal precipitation over Libya are more strikingly experienced from 1976-2000 than from 1951-1975 indicating a growing magnitude of climate change in more recent times. Negative trends of mean annual relative humidity were computed at eight stations, while positive trends prevailed at seven stations from 1946-2000. For the short observation period 1976-2000, positive trends were computed at most stations. Annual cloud amount totals decreased at most study stations in Libya over both long and short periods. Re-markably large spatial variations of climate changes were observed from north to south over Libya. Causes of climate change were discussed showing high correlation between tempera-ture increasing over Libya and CO2 emissions; weakly positive correlation between pre-cipitation and North Atlantic Oscillation index; negative correlation between temperature and sunspot numbers; negative correlation between precipitation over Libya and Southern Oscillation Index. The years 1992 and 1993 were shown as the coldest in the 1990s result-ing from the eruption of Mount Pinatubo, 1991. Libya is affected by climate change in many ways, in particular, crop production and food security, water resources, human health, population settlement and biodiversity. But the effects of climate change depend on its magnitude and the rate with which it occurs. Jifara Plain, located in northwestern Libya, has been seriously exposed to desertifica-tion as a result of climate change, landforms, overgrazing, over-cultivation and population growth. Soils have been degraded, vegetation cover disappeared and the groundwater wells were getting dry in many parts. The effect of desertification on Jifara Plain appears through reducing soil fertility and crop productivity, leading to long-term declines in agri-cultural yields, livestock yields, plant standing biomass, and plant biodiversity. Desertifi-cation has also significant implications on livestock industry and the national economy. Desertification accelerates migration from rural and nomadic areas to urban areas as the land cannot support the original inhabitants. In the absence of major shifts in policy, economic growth, energy prices, and con-sumer trends, climate change in Libya and desertification of Jifara Plain are expected to continue in the future. Libya cooperated with United Nations and other international organizations. It has signed and ratified a number of international and regional agreements which effectively established a policy framework for actions to mitigate climate change and combat deserti-fication. Libya has implemented several laws and legislative acts, with a number of ancil-lary and supplementary rules to regulate. Despite the current efforts and ongoing projects being undertaken in Libya in the field of climate change and desertification, urgent actions and projects are needed to mitigate climate change and combat desertification in the near future.