Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Impact of forest fragmentation and disturbance on the endangered tropical tree Prunus africana (Rosaceae)

Anthropogene Fragmentierung und Störung von Wäldern beeinflussen ökologische Prozesse. Darüber hinaus werden genetische Drift und Inzucht verstärkt und die Fitness von Populationen beeinträchtigt. Um die Einflüsse von Fragmentierung und Störung auf die Biodiversität und Prozesse in tropischen Wäldern zu ermitteln, habe ich im „Kakamega Forest“, West-Kenia, die Baumart Prunus africana genauer untersucht. Dabei lag der Fokus auf (i) der Frugivorengemeinschaft und Samenausbreitung, (ii) der Kleinsäugergemeinschaft im Kontext der Samenprädation und (iii) der genetische Populationsstruktur von Keimlingen und adulten Bäumen. Der Vergleich von Keimlingen mit adulten Bäumen ermöglicht es, Veränderungen im Genfluss zwischen Generationen festzustellen. Die Ergebnisse zeigten, dass im untersuchten Waldgebiet insgesamt 49 frugivore Arten (Affen und Vögel) vorkommen. Dabei lag die Gesamtartenzahl im zusammenhängenden Wald höher als in den isoliert liegenden Fragmenten. An den Früchten von P. africana konnten insgesamt 36 Arten fressend beobachtet werden. Hier jedoch wurden in Fragmenten eine leicht erhöhte Frugivorenzahl sowie marginal signifikant erhöhte Samenausbreitungsraten nachgewiesen. Der Vergleich von stark gestörten mit weniger gestörten Flächen zeigte eine höhere Gesamtartenzahl sowie eine signifikant höhere Frugivorenzahl in P. africana in stark gestörten Flächen. Entsprechend war die Samenausbreitungsrate in stark gestörten Flächen marginal signifikant erhöht. Diese Ergebnisse deuten darauf hin, dass die quantitative Samenausbreitung in fragmentierten und gestörten Flächen etwas erhöht ist und somit eine gewisse Artenredundanz besteht, die den Verlust einzelner Arten ausgleichen könnte. Prunus africana Samen, die auf dem Boden lagen, wurden hauptsächlich von einer Nagerart (Praomys cf. jacksonii) erbeutet. Dabei war in gestörten Waldbereichen eine tendenziell höhere Prädatoraktivität zu beobachten als in weniger gestörten. Zudem waren einzelne Samen im Gegensatz zu Samengruppen in gestörten Flächen signifikant höherem Prädationsdruck ausgesetzt. Diese Ergebnisse zeigen, dass Fragmentierung sowie anthropogene Störungen auf unterschiedliche Prozesse im Lebenszyklus eines tropischen Baumes gegensätzliche Effekte haben können. Eine Extrapolation von einem auf einen anderen Prozess kann somit nicht erfolgen. Die genetische Differenzierung der adulten Baumpopulationen war gering (FST = 0.026). Der Großteil ihrer Variation (~ 97 %) lag innerhalb der Populationen, was intensiven Genfluss in der Vergangenheit widerspiegelt. Die genetische Differenzierung der Keimlinge war etwas erhöht (FST = 0.086) und ~ 91 % ihrer Variation lag innerhalb der Populationen. Im Gegensatz zu den adulten Bäumen konnte ich für Keimlinge ein „Isolation-by-distance“-Muster feststellen. Somit sind erste Hinweise auf begrenzten Genfluss im Keimlingsstadium infolge von Fragmentierung gegeben. Obwohl die Momentaufnahmen im Freiland keine Abnahme in der Frugivorenzahl und Samenausbreitung von P. africana als Folge von Fragmentierung beobachten ließen, weisen die Ergebnisse der genetischen Studie auf einen bereits reduzierten Genaustausch zwischen den Populationen hin. Somit lässt sich feststellen, dass die Faktoren Fragmentierung und Störung genetische Diversität, ökologische Prozesse und Artendiversität in Wäldern jeweils auf unterschiedliche Weise beeinflussen. Um Konsequenzen derartiger Einflüsse folgerichtig abschätzen zu können, sind Studien auf unterschiedlichen Diversitätsebenen unabdingbar.

Growth, modification and integration of carbon nanotubes into molecular electronics

Molecules are the smallest possible elements for electronic devices, with active elements for such devices typically a few Angstroms in footprint area. Owing to the possibility of producing ultrahigh density devices, tremendous effort has been invested in producing electronic junctions by using various types of molecules. The major issues for molecular electronics include (1) developing an effective scheme to connect molecules with the present micro- and nano-technology, (2) increasing the lifetime and stabilities of the devices, and (3) increasing their performance in comparison to the state-of-the-art devices. In this work, we attempt to use carbon nanotubes (CNTs) as the interconnecting nanoelectrodes between molecules and microelectrodes. The ultimate goal is to use two individual CNTs to sandwich molecules in a cross-bar configuration while having these CNTs connected with microelectrodes such that the junction displays the electronic character of the molecule chosen. We have successfully developed an effective scheme to connect molecules with CNTs, which is scalable to arrays of molecular electronic devices. To realize this far reaching goal, the following technical topics have been investigated. 1. Synthesis of multi-walled carbon nanotubes (MWCNTs) by thermal chemical vapor deposition (T-CVD) and plasma-enhanced chemical vapor deposition (PECVD) techniques (Chapter 3). We have evaluated the potential use of tubular and bamboo-like MWCNTs grown by T-CVD and PE-CVD in terms of their structural properties. 2. Horizontal dispersion of MWCNTs with and without surfactants, and the integration of MWCNTs to microelectrodes using deposition by dielectrophoresis (DEP) (Chapter 4). We have systematically studied the use of surfactant molecules to disperse and horizontally align MWCNTs on substrates. In addition, DEP is shown to produce impurityfree placement of MWCNTs, forming connections between microelectrodes. We demonstrate the deposition density is tunable by both AC field strength and AC field frequency. 3. Etching of MWCNTs for the impurity-free nanoelectrodes (Chapter 5). We show that the residual Ni catalyst on MWCNTs can be removed by acid etching; the tip removal and collapsing of tubes into pyramids enhances the stability of field emission from the tube arrays. The acid-etching process can be used to functionalize the MWCNTs, which was used to make our initial CNT-nanoelectrode glucose sensors. Finally, lessons learned trying to perform spectroscopic analysis of the functionalized MWCNTs were vital for designing our final devices. 4. Molecular junction design and electrochemical synthesis of biphenyl molecules on carbon microelectrodes for all-carbon molecular devices (Chapter 6). Utilizing the experience gained on the work done so far, our final device design is described. We demonstrate the capability of preparing patterned glassy carbon films to serve as the bottom electrode in the new geometry. However, the molecular switching behavior of biphenyl was not observed by scanning tunneling microscopy (STM), mercury drop or fabricated glassy carbon/biphenyl/MWCNT junctions. Either the density of these molecules is not optimum for effective integration of devices using MWCNTs as the nanoelectrodes, or an electroactive contaminant was reduced instead of the ionic biphenyl species. 5. Self-assembly of octadecanethiol (ODT) molecules on gold microelectrodes for functional molecular devices (Chapter 7). We have realized an effective scheme to produce Au/ODT/MWCNT junctions by spanning MWCNTs across ODT-functionalized microelectrodes. A percentage of the resulting junctions retain the expected character of an ODT monolayer. While the process is not yet optimized, our successful junctions show that molecular electronic devices can be fabricated using simple processes such as photolithography, self-assembled monolayers and dielectrophoresis.

Habitat fragmentation and adaptation: a reciprocal replant-transplant experiment among 15 populations of Lychnis flos-cuculi

1. Habitat fragmentation and variation in habitat quality can both affect plant performance, but their effects have rarely been studied in combination. We thus examined plant performance in response to differences in habitat quality for a species subject to habitat fragmentation, the common but declining perennial herb Lychnis flos-cuculi. 2. We reciprocally transplanted plants between 15 fen grasslands in north-east Switzerland and recorded plant performance for 4 years. 3. Variation between the 15 target sites was the most important factor and affected all measures of plant performance in all years. This demonstrates the importance of plastic responses to habitat quality for plant performance. 4. Plants from smaller populations produced fewer rosettes than plants from larger populations in the first year of the replant-transplant experiment. 5. Plant performance decreased with increasing ecological difference between grassland of origin and target grassland, indicating adaptation to ecological conditions. In contrast, plant performance was not influenced by microsatellite distance and hardly by geographic distance between grassland of origin and target grassland. 6. Plants originating from larger populations were better able to cope with larger ecological differences between transplantation site and site of origin. 7. Synthesis: In addition to the direct effects of target grasslands, both habitat fragmentation, through reduced population size, and adaptation to habitats of different quality, contributed to the performance of L. flos-cuculi. This underlines that habitat fragmentation also affects species that are still common. Moreover, it suggests that restoration projects involving L. flos-cuculi should use plant material from large populations living in habitats similar to the restoration site. Finally, our results bring into question whether plants in small habitat remnants will be able to cope with future environmental change.

Europe and Islam: Alarmists, Victimists, and Integration by Law

This article reviews the minefield of Muslim integration in Europe, paying special attention to the legal integration of Islam, which has not yet found the attention that it deserves. In a first step, the article contrasts ‘victimist’ and ‘alarmist’ views on contemporary Muslim integration, both of which are found misleading. Instead, as argued in the second part, significant progress has been made through the legal route. The conclusion provides a reflection on the role of Islam for Europe’s ‘liberal identity’ today.

Cue Recognition and Integration - Eye Tracking Evidence of Processing Differences in Sentence Comprehension in Aphasia

PURPOSE: We aimed at further elucidating whether aphasic patients' difficulties in understanding non-canonical sentence structures, such as Passive or Object-Verb-Subject sentences, can be attributed to impaired morphosyntactic cue recognition, and to problems in integrating competing interpretations. METHODS: A sentence-picture matching task with canonical and non-canonical spoken sentences was performed using concurrent eye tracking. Accuracy, reaction time, and eye tracking data (fixations) of 50 healthy subjects and 12 aphasic patients were analysed. RESULTS: Patients showed increased error rates and reaction times, as well as delayed fixation preferences for target pictures in non-canonical sentences. Patients' fixation patterns differed from healthy controls and revealed deficits in recognizing and immediately integrating morphosyntactic cues. CONCLUSION: Our study corroborates the notion that difficulties in understanding syntactically complex sentences are attributable to a processing deficit encompassing delayed and therefore impaired recognition and integration of cues, as well as increased competition between interpretations.