Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

Causes of legume-rotation effects in increasing cereal yields across the Sudanian, Sahelian and Guinean zone of West Africa

On-farm experiments and pot trials were conducted on eight West African soils to explore the mechanisms governing the often reported legume rotation-induced cereal growth increases in this region. Crops comprised pearl millet (Pennisetum glaucum L.), sorghum (Sorghum bicolor Moench), maize (Zea mays L.), cowpea (Vigna unguiculata Walp.) and groundnut (Arachis hypogaea L.). In groundnut trials the observed 26 to 85% increases in total dry matter (TDM) of rotation cereals (RC) compared with continuous cereals (CC) in the 4th year appeared to be triggered by site- and crop-specific early season differences in nematode infestation (up to 6-fold lower in RC than in CC), enhanced Nmin and a 7% increase in mycorrhizal (AM) infection. In cowpea trials yield effects on millet and differences in nematode numbers, Nmin and AM were much smaller. Rhizosphere studies indicated effects on pH and acid phosphatase activity as secondary causes for the observed growth differences between RC and CC. In the study region legume-rotation effects on cereals seemed to depend on the capability of the legume to suppress nematodes and to enhance early N and P availability for the subsequent cereal.

Cereal/legume rotation effects on rhizosphere bacterial community structure in West African soils

The increased use of cereal/legume crop rotation has been advocated as a strategy to increase cereal yields of subsistence farmers in West Africa, and is believed to promote changes in the rhizosphere that enhance early plant growth. In this study we investigated the microbial diversity of the rhizoplane from seedlings grown in two soils previously planted to cereal or legume from experimental plots in Gaya, Niger, and Kaboli, Togo. Soils from these legume rotation and continuous cereal plots were placed into containers and sown in a growth chamber with maize (Zea mays L.), millet (Pennisetum glaucum L.), sorghum (Sorghum bicolor L. Moench.), cowpea (Vigna unguiculata L.) or groundnut (Arachis hypogaea L.). At 7 and 14 days after sowing, 16S rDNA profiles of the eubacterial and ammoniaoxidizing communities from the rhizoplane and bulk soil were generated using denaturing gradient gel electrophoresis (DGGE). Community profiles were subjected to peak fitting analyses to quantify the DNA band position and intensities, after which these data were compared using correspondence and principal components analysis. The data showed that cropping system had a highly significant effect on community structure (p <0.005), irrespective of plant species or sampling time. Continuous cereal-soil grown plants had highly similar rhizoplane communities across crop species and sites, whereas communities from the rotation soil showed greater variability and clustered with respect to plant species. Analyses of the ammonia-oxidizing communities provided no evidence of any effects of plant species or management history on ammonia oxidizers in soil from Kaboli, but there were large shifts with respect to this group of bacteria in soils from Gaya. The results of these analyses show that crop rotation can cause significant shifts in rhizosphere bacterial communities.

Legume rotation effects on early growth and rhizosphere microbiology of sorghum in West African soils

Cereal yield increases in legume rotations on west African soils were the subject of much recent research aiming at the development of more productive cropping systems for the mainly subsistence-oriented agriculture in this region. However, little has been done to elucidate the possible contribution of soil microbiological factors to these rotation effects. Therefore a pot trial was conducted using legume rotation and continuous cereal soils each from one site in Burkina Faso and two sites in Togo where cropping system experiments had been conducted over 4 yrs. All soils were planted with seedlings of sorghum (Sorghum bicolor L. Moench). From 21 days after sowing onwards relative growth rates in rotation soils were higher than in the continuous cereal soils, resulting in between 69 and 500% higher shoot dry matter of rotation sorghum compared to sorghum growing in continuous cereal soils. Across sites rotation soils were characterized by higher pH, higher microbial N and a lower microbial biomass C/N ratio and, with the exception of one site, a higher fungal biomass in the rhizosphere. The bacterial and eukaryal community structure in the soil, assessed by denaturing gradient gel electrophoresis (DGGE), differed between sites. However, only at one site differed the bacterial and the eukaryal community structure in the rotation soil significantly from that in the continuous cereal soil. Although the results of this study confirmed the marked plantgrowth differences between sub-Saharan legume-rotation soils and their continuous cereal counterparts they also showed the difficulties to differentiate possible microbiological causes from their effects.

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Algorithms for Tamagawa Number Conjectures

In dieser Arbeit werden Algorithmen zur Untersuchung der äquivarianten Tamagawazahlvermutung von Burns und Flach entwickelt. Zunächst werden Algorithmen angegeben mit denen die lokale Fundamentalklasse, die globale Fundamentalklasse und Tates kanonische Klasse berechnet werden können. Dies ermöglicht unter anderem Berechnungen in Brauergruppen von Zahlkörpererweiterungen. Anschließend werden diese Algorithmen auf die Tamagawazahlvermutung angewendet. Die Epsilonkonstantenvermutung kann dadurch für alle Galoiserweiterungen L|K bewiesen werden, bei denen L in einer Galoiserweiterung E|Q vom Grad kleiner gleich 15 eingebettet werden kann. Für die Tamagawazahlvermutung an der Stelle 1 wird ein Algorithmus angegeben, der die Vermutung für ein gegebenes Fallbeispiel L|Q numerischen verifizieren kann. Im Spezialfall, dass alle Charaktere rational oder abelsch sind, kann dieser Algorithmus die Vermutung für L|Q sogar beweisen.

Development and Integration of Biocontrol Products in Branched Broomrape (Phelipanche ramosa) management in Tomato

Parasitic weeds of the genera Striga, Orobanche, and Phelipanche pose a severe problem for agriculture because they are difficult to control and are highly destructive to several crops. The present work was carried out during the period October, 2009 to February, 2012 to evaluate the potential of arbuscular mycorrhizal fungi (AMF) to suppress P. ramosa on tomatoes and to investigate the effects of air-dried powder and aqueous extracts from Euphorbia hirta on germination and haustorium initiation in Phelipanche ramosa. The work was divided into three parts: a survey of the indigenous mycorrhizal flora in Sudan, second, laboratory and greenhouse experiments (conducted in Germany and Sudan) to construct a base for the third part, which was a field trial in Sudan. A survey was performed in 2009 in the White Nile state, Sudan to assess AMF spore densities and root colonization in nine fields planted with 13 different important agricultural crops. In addition, an attempt was made to study the relationship between soil physico-chemical properties and AMF spore density, colonization rate, species richness and other diversity indices. The mean percentage of AMF colonization was 34%, ranging from 19-50%. The spore densities (expressed as per 100 g dry soil) retrieved from the rhizosphere of different crops were relatively high, varying from 344 to 1222 with a mean of 798. There was no correlation between spore densities in soil and root colonization percentage. A total of 45 morphologically classifiable species representing ten genera of AMF were detected with no correlation between the number of species found in a soil sample and the spore density. The most abundant genus was Glomus (20 species). The AMF diversity expressed by the Shannon–Weaver index was highest in sorghum (H\= 2.27) and Jews mallow (H\= 2.13) and lowest in alfalfa (H\= 1.4). With respect to crop species, the genera Glomus and Entrophospora were encountered in almost all crops, except for Entrophospora in alfalfa. Kuklospora was found only in sugarcane and sorghum. The genus Ambispora was recovered only in mint and okra, while mint and onion were the only species on which no Acaulospora was found. The hierarchical cluster analysis based on the similarity among AMF communities with respect to crop species overall showed that species compositions were relatively similar with the highest dissimilarity of about 25% separating three of the mango samples and the four sorghum samples from all other samples. Laboratory experiments studied the influence of root and stem exudates of three tomato varieties infected by three different Glomus species on germination of P. ramosa. Root exudates were collected 21or 42 days after transplanting (DAT) and stem exudates 42 DAT and tested for their effects on germination of P. ramosa seeds in vitro. The tomato varieties studied did not have an effect on either mycorrhizal colonization or Phelipanche germination. Germination in response to exudates from 42 day old mycorrhizal plants was significantly reduced in comparison to non-mycorrhizal controls. Germination of P. ramosa in response to root exudates from 21 day old plants was consistently higher than for 42 day-old plants (F=121.6; P<.0001). Stem diffusates from non-mycorrhizal plants invariably elicited higher germination than diffusates from the corresponding mycorrhizal ones and differences were mostly statistically significant. A series of laboratory experiments was undertaken to investigate the effects of aqueous extracts from Euphorbia hirta on germination, radicle elongation, and haustorium initiation in P. ramosa. P. ramosa seeds conditioned in water and subsequently treated with diluted E. hirta extract (10-25% v/v) displayed considerable germination (47-62%). Increasing extract concentration to 50% or more reduced germination in response to the synthetic germination stimulants GR24 and Nijmegen-1 in a concentration dependent manner. P. ramosa germlings treated with diluted Euphorbia extract (10-75 % v/v) displayed haustorium initiation comparable to 2, 5-Dimethoxy-p-benzoquinon (DMBQ) at 20 µM. Euphorbia extract applied during conditioning reduced haustorium initiation in a concentration dependent manner. E. hirta extract or air-dried powder, applied to soil, induced considerable P. ramosa germination. Pot experiments were undertaken in a glasshouse at the University of Kassel, Germany, to investigate the effects of P. ramosa seed bank on tomato growth parameters. Different Phelipanche seed banks were established by mixing the parasite seeds (0 - 32 mg) with the potting medium in each pot. P. ramosa reduced all tomato growth parameters measured and the reduction progressively increased with seed bank. Root and total dry matter accumulation per tomato plant were most affected. P. ramosa emergence, number of tubercles, and tubercle dry weight increased with the seed bank and were, invariably, maximal with the highest seed bank. Another objective was to determine if different AM fungi differ in their effects on the colonization of tomatoes with P. ramosa and the performance of P. ramosa after colonization. Three AMF species viz. GIomus intraradices, Glomus mosseae and Glomus Sprint® were used in this study. For the infection, P. ramosa seeds (8 mg) were mixed with the top 5 cm soil in each pot. No mycorrhizal colonization was detected in un-inoculated control plants. P. ramosa infested, mycorrhiza inoculated tomato plants had significantly lower AMF colonization compared to plants not infested with P. ramosa. Inoculation with G. intraradices, G. mosseae and Glomus Sprint® reduced the number of emerged P. ramosa plants by 29.3, 45.3 and 62.7% and the number of tubercles by 22.2, 42 and 56.8%, respectively. Mycorrhizal root colonization was positively correlated with number of branches and total dry matter of tomatoes. Field experiments on tomato undertaken in 2010/12 were only partially successful because of insect infestations which resulted in the complete destruction of the second run of the experiment. The effects of the inoculation with AMF, the addition of 10 t ha-1 filter mud (FM), an organic residues from sugar processing and 36 or 72 kg N ha-1 on the infestation of tomatoes with P. ramosa were assessed. In un-inoculated control plants, AMF colonization ranged between 13.4 to 22.1% with no significant differences among FM and N treatments. Adding AMF or FM resulted in a significant increase of branching in the tomato plants with no additive effects. Dry weights were slightly increased through FM application when no N was applied and significantly at 36 kg N ha-1. There was no effect of FM on the time until the first Phelipanche emerged while AMF and N application interacted. Especially AMF inoculation resulted in a tendency to delayed P. ramosa emergence. The marketable yield was extremely low due to the strong fruit infestation with insects mainly whitefly Bemisia tabaci and tomato leaf miner (Tuta absoluta). Tomatoes inoculated with varied mycorrhiza species displayed different response to the insect infestation, as G. intraradices significantly reduced the infestation, while G. mosseae elicited higher insect infestation. The results of the present thesis indicate that there may be a potential of developing management strategies for P. ramosa targeting the pre-attachment stage namely germination and haustorial initiation using plant extracts. However, ways of practical use need to be developed. If such treatments can be combined with AMF inoculation also needs to be investigated. Overall, it will require a systematic approach to develop management tools that are easily applicable and affordable to Sudanese farmers. It is well-known that proper agronomical practices such as the design of an optimum crop rotation in cropping systems, reduced tillage, promotion of cover crops, the introduction of multi-microbial inoculants, and maintenance of proper phosphorus levels are advantageous if the mycorrhiza protection method is exploited against Phelipanche ramosa infestation. Without the knowledge about the biology of the parasitic weeds by the farmers and basic preventive measures such as hygiene and seed quality control no control strategy will be successful, however.

Pathogens occuring in the winter pea-maize-winter wheat rotation, their host specificity and the potential of compost in suppressing foot and root disease of peas

The overall aim of the work presented was to evaluate soil health management with a specific focus on soil borne diseases of peas. For that purpose field experiments were carried out from 2009 until 2013 to assess crop performance and pathogen occurrence in the rotation winter pea-maize-winter wheat and if the application of composts can improve system performance. The winter peas were left untreated or inoculated with Phoma medicaginis, in the presence or absence of yard waste compost at rate of 5 t dry matter ha-1. A second application of compost was made to the winter wheat. Fusarium ssp. were isolated and identified from the roots of all three crops and the Ascochyta complex pathogens on peas. Bioassays were conducted under controlled conditions to assess susceptibility of two peas to Fusarium avenaceum, F. solani, P. medicaginis and Didymella pinodes and of nine plant species to F. avenaceum. Also, effects of compost applications and temperature on pea diseases were assessed. Application of composts overall stabilized crop performance but it did not lead to significant yield increases nor did it affect pathogen composition and occurrence. Phoma medicaginis was dominating the pathogen complex on peas. F. graminearum, F. culmorum, F. proliferatum, Microdochium nivale, F. crookwellense, F. sambucinum, F. oxysporum, F. avenaceum and F. equiseti were frequently isolated species from maize and winter wheat with no obvious influence of the pre-crop on the Fusarium species composition. The spring pea Santana was considerably more susceptible to the pathogens tested than the winter pea EFB33 in both sterile sand and non-sterilized field soil. F. avenaceum was the most aggressive pathogen, followed by P. medicaginis, D. pinodes, and F. solani. Aggressiveness of all pathogens was greatly reduced in non-sterile field soil. F. avenaceum caused severe symptoms on roots of all nine plant species tested. Especially susceptible were Trifolium repens, T. subterraneum, Brassica juncea and Sinapis alba in addition to peas. Reduction of growing temperatures from 19/16°C day/night to 16/12°C and 13/10°C did not affect the efficacy of compost. It reduced plant growth and slightly increased disease on EFB33 whereas the highest disease severity on Santana was observed at the highest temperature, 19/16°C. Application of 20% v/v of compost reduced disease on peas due to all four pathogens depending on pea variety, pathogen and growing media used. Suppression was also achieved with lower application rate of 3.5% v/v. Tests with γ sterilized compost suggest that the suppression of disease caused by Fusarium spp. is biological in origin, whereas chemical and physical properties of compost are playing an additional role in the suppression of disease caused by D. pinodes and P. medicaginis.

Internal Camera Calibration Using Rotation and Geometric Shapes

This paper describes a simple method for internal camera calibration for computer vision. This method is based on tracking image features through a sequence of images while the camera undergoes pure rotation. The location of the features relative to the camera or to each other need not be known and therefore this method can be used both for laboratory calibration and for self calibration in autonomous robots working in unstructured environments. A second method of calibration is also presented. This method uses simple geometric objects such as spheres and straight lines to The camera parameters. Calibration is performed using both methods and the results compared.

Rotation Invariant Real-time Face Detection and Recognition System

In this report, a face recognition system that is capable of detecting and recognizing frontal and rotated faces was developed. Two face recognition methods focusing on the aspect of pose invariance are presented and evaluated - the whole face approach and the component-based approach. The main challenge of this project is to develop a system that is able to identify faces under different viewing angles in realtime. The development of such a system will enhance the capability and robustness of current face recognition technology. The whole-face approach recognizes faces by classifying a single feature vector consisting of the gray values of the whole face image. The component-based approach first locates the facial components and extracts them. These components are normalized and combined into a single feature vector for classification. The Support Vector Machine (SVM) is used as the classifier for both approaches. Extensive tests with respect to the robustness against pose changes are performed on a database that includes faces rotated up to about 40 degrees in depth. The component-based approach clearly outperforms the whole-face approach on all tests. Although this approach isproven to be more reliable, it is still too slow for real-time applications. That is the reason why a real-time face recognition system using the whole-face approach is implemented to recognize people in color video sequences.

Translation Invariance in Object Recognition, and Its Relation to Other Visual Transformations

Human object recognition is generally considered to tolerate changes of the stimulus position in the visual field. A number of recent studies, however, have cast doubt on the completeness of translation invariance. In a new series of experiments we tried to investigate whether positional specificity of short-term memory is a general property of visual perception. We tested same/different discrimination of computer graphics models that were displayed at the same or at different locations of the visual field, and found complete translation invariance, regardless of the similarity of the animals and irrespective of direction and size of the displacement (Exp. 1 and 2). Decisions were strongly biased towards same decisions if stimuli appeared at a constant location, while after translation subjects displayed a tendency towards different decisions. Even if the spatial order of animal limbs was randomized ("scrambled animals"), no deteriorating effect of shifts in the field of view could be detected (Exp. 3). However, if the influence of single features was reduced (Exp. 4 and 5) small but significant effects of translation could be obtained. Under conditions that do not reveal an influence of translation, rotation in depth strongly interferes with recognition (Exp. 6). Changes of stimulus size did not reduce performance (Exp. 7). Tolerance to these object transformations seems to rely on different brain mechanisms, with translation and scale invariance being achieved in principle, while rotation invariance is not.

Rotation Invariant Object Recognition from One Training Example

Local descriptors are increasingly used for the task of object recognition because of their perceived robustness with respect to occlusions and to global geometrical deformations. Such a descriptor--based on a set of oriented Gaussian derivative filters-- is used in our recognition system. We report here an evaluation of several techniques for orientation estimation to achieve rotation invariance of the descriptor. We also describe feature selection based on a single training image. Virtual images are generated by rotating and rescaling the image and robust features are selected. The results confirm robust performance in cluttered scenes, in the presence of partial occlusions, and when the object is embedded in different backgrounds.