Groups with torsion, bordism and rho-invariants

Let G be a discrete group, and let M be a closed spin manifold of dimension m>3 with pi_1(M)=G. We assume that M admits a Riemannian metric of positive scalar curvature. We discuss how to use the L2-rho invariant and the delocalized eta invariant associated to the Dirac operator on M in order to get information about the space of metrics with positive scalar curvatur1e. In particular we prove that, if G contains torsion and M is congruent 3 mod 4 then M admits infinitely many different bordism classes of metrics with positive scalar curvature. We show that this is true even up to diffeomorphism. If G has certain special properties then we obtain more refined information about the ``size'' of the space of metric of positive scalar curvature, and these results also apply if the dimension is congruent to 1 mod 4. For example, if G contains a central element of odd order, then the moduli space of metrics of positive scalar curvature has infinitely many components, if it is not empty. Some of our invariants are the delocalized eta-invariants introduced by John Lott. These invariants are defined by certain integrals whose convergence is not clear in general, and we show, in effect, that examples exist where this integral definitely does not converge, thus answering a question of Lott. We also discuss the possible values of the rho invariants of the Dirac operator and show that there are certain global restrictions (provided the scalar curvature is positive).Comment: 21 pages; comma in metadata (author field) added. final version to appear in Pacific Journal of Mathematic

A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture

Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with $\pi_1(M) = Z^4times Z/3$, so that the index invariant in the KO-theory of the reduced $C^*$-algebra of $\pi_1(M)$ is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifolds cannot carry a metric of positive scalar curvature. The existence of such a metric is predicted by the (unstable) Gromov-Lawson-Rosenberg conjecture.Comment: 4 pages, ol

Permanent Superhumps in V1974 Cyg

We present results of 32 nights of CCD photometry of V1974 Cygni, from the years 1994 and 1995. We verify the presence of two distinct periodicities in the light curve: 0.0812585 day~1.95 hours and 0.0849767 d~2.04 hr. We establish that the shorter periodicity is the orbital period of the underlying binary system. The longer period oscillates with an average value of |dot(P)| ~ 3x10^(7)--typical to permanent superhumps. The two periods obey the linear relation between the orbital and superhump periods that holds among members of the SU Ursae Majoris class of dwarf novae. A third periodicity of 0.083204 d~2.00 hr appeared in 1994 but not in 1995. It may be related to the recently discovered anti-superhump phenomenon. These results suggest a linkage between the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence of an accretion disk and permanent superhumps in the system no later than 30 months after the nova outburst. From the precessing disk model of the superhump phenomenon we estimate that the mass ratio in the binary system is between 2.2 and 3.6. Combined with previous results this implies a white dwarf mass of 0.75-1.07 M sun.Comment: 11 pages, 10 eps. figures, Latex, accepted for publication in MNRA

Root enhancement in cytokinin-deficient oilseed rape causes leaf mineral enrichment, increases the chlorophyll concentration under nutrient limitation and enhances the phytoremediation capacity

Background Cytokinin is a negative regulator of root growth, and a reduction of the cytokinin content or signalling causes the formation a larger root system in model plants, improves their growth under drought and nutrient limitation and causes increased accumulation of elements in the shoot. Roots are an important but understudied target of plant breeding. Here we have therefore explored whether root enhancement by lowering the cytokinin content can also be achieved in oilseed rape (Brassica napus L.) plants. Results Transgenic plants overexpressing the CKX2 gene of Arabidopsis thaliana encoding a cytokinin-degrading cytokinin oxidase/dehydrogenase showed higher CKX activity and a strongly reduced cytokinin content. Cytokinin deficiency led to the formation of a larger root system under different growth conditions, which was mainly due to an increased number of lateral and adventitious roots. In contrast, shoot growth was comparable to wild type, which caused an enhanced root-to-shoot ratio. Transgenic plants accumulated in their leaves higher concentrations of macro- and microelements including P, Ca, Mg, S, Zn, Cu, Mo and Mn. They formed more chlorophyll under Mg- and S-deficiency and accumulated a larger amount of Cd and Zn from contaminated medium and soil. Conclusions These findings demonstrate the usefulness of ectopic CKX gene expression to achieve root enhancement in oilseed rape and underpin the functional relevance of a larger root system. Furthermore, the lack of major developmental consequences on shoot growth in cytokinin-deficient oilseed rape indicates species-specific differences of CKX gene and/or cytokinin action

Descending Octopaminergic Neurons in the Stick Insect: Their Inputs and their Output Effects on the Locomotor System

The neural networks controlling locomotion (walking) must exhibit a high degree of flexibility for task-specific adaptation of behavior to environmental influences and changes in internal state. Neuromodulatory influences are very important for this flexibility, as they can regulate the activity of all neurons in the walking system and the strengths of their synaptic connections. To fully understand the neural control of walking, it is crucial to identify the neurons that release neuromodulators and to determine their activity patterns during behavior and analyze the properties of their output effects. Octopamine, one such neuromodulator, is considered the invertebrate homolog to the vertebrate noradrenaline. It is a significant modulator in insect locomotor systems, both acting in the peripheral and central nervous systems. Octopamine modulates muscle metabolism, neuromuscular transmission, sensory sensitivity, excitability of motor neurons, and activity in the central pattern generating networks that control locomotion. The neural source of octopamine acting in the central nervous system of insect thoracic segments has not yet been identified. Thus, it is unknown to what extent effects of application of octopamine to thoracic ganglia in previous studies reflect the physiological role of octopamine. In the current thesis, I hypothesized that dorsal unpaired median neurons with bilaterally descending axons (desDUM neurons) are a source of octopaminergic modulation of activity in thoracic neural networks for the control of walking in the stick insect Carausius morosus. I revealed the morphology of desDUM neurons in the gnathal ganglion by intracellular staining. Employing the newly developed method of direct MALDI-TOF mass spectrometry, I could show that stick insect desDUM neurons are octopaminergic. Using semi-intact preparations and intracellular recordings of desDUM neurons, I found that they are phasically activated during six-legged walking and single-leg stepping. The phasic excitatory input to desDUM neurons during walking does not arise from coupling to activity of mesothoracic central pattern generating networks, but most likely from activation of mechanosensory organs of all six legs. Passive leg movement and stimulation of mesothoracic campaniform sensilla excited desDUM neurons. Furthermore, stimulation of the mesothoracic femoral chordotonal organ (fCO) had a weak excitatory influence on their activity. Further, I investigated the output effects of desDUM neurons on reflex-evoked, spontaneous, and centrally generated activity of mesothoracic motor neurons with activation of single desDUM neurons. I could show that distinct desDUM neurons mediate differential effects. Some neurons induce a decrease and others an increase, in the magnitude of reflex-induced motor neuron activity. The neurons which mediated an excitatory influence additionally increased the frequency of reversal of an fCO-induced postural reflex. Some desDUM neurons mediated an increase in the frequency of centrally generated rhythmic motor neuron activity. Collectively, the results of the current thesis provide a comprehensive characterization of desDUM neurons and their complex roles in the stick insect locomotor system. The identity of direct neural target structures for the modulatory action of desDUM neurons, as well as the net output effects of the entire population of desDUM neurons during walking remain open questions. In future experiments, genetic access to desDUM neurons could aid in the activation, silencing, or visualization of their activity, which would collectively contribute to comprehensive answers to the open questions

Prognostic significance of DNA cytometry in cutaneous malignant lymphomas.

The current classification of cutaneous malignant lymphomas (ML) into low-grade and high-grade lymphomas was found to be of limited reproducibility and permitted only a rough prediction about outcome. With this in mind, the relationship between nuclear DNA content and both prognosis and histologic grading according to the Kiel classification was evaluated on Feulgen-stained imprint specimens. In all, 49 cases of malignant non-Hodgkin's lymphoma, primary of the skin or with an involvement of the skin as one of the first symptoms, were studied using a computerized high-resolution image analysis system. The 2c deviation index (2cDI), which reflects the variation of the nuclear DNA values around the normal diploid peak, was found to be the best prognostically relevant criterion. Using the 2cDI, a significant discrimination (P less than 0.001 in the U test) between low-grade and high-grade ML was achieved. The prognostic benefit of the 2cDI was well documented by a significant inverse correlation between the 2cDI and the period of time until the patients progressed at least into one higher stage or died of lymphoma (r equals -0.63, P less than 0.05). In addition, the 2cDI enabled prognosis of the course of disease. In the group with low 2cDI values (2cDI, less than 0.5), no progression of the disease was observed after 1 year. In the groups presenting with a 2cDI between 0.5 and 1.0 and higher than 1.0, a progression was found in 57% and 64% of the cases studied, respectively. In conclusion, these measurements indicate that the determination of DNA distribution patterns in imprint specimens allows a precise and objective prognostic evaluation of cutaneous ML

The Arabidopsis TUMOR PRONE5 (TUP5) gene encodes an acetylornithine aminotransferase required for arginine biosynthesis and root meristem maintenance in blue light.

Arginine is an essential amino acid necessary for protein synthesis and is also a nitrogen storage compound. The genes encoding the enzymes of arginine biosynthesis in plants are not well characterized and have mainly been predicted from homologies to bacterial and fungal genes. We report the cloning and characterization of the TUMOR PRONE5 (TUP5) gene of Arabidopsis (Arabidopsis thaliana) encoding an acetylornithine aminotransferase (ACOAT), catalyzing the fourth step of arginine biosynthesis. The free arginine content was strongly reduced in the chemically induced recessive mutant tup5-1, root growth was restored by supplementation with arginine and its metabolic precursors, and a yeast (Saccharomyces cerevisiae) ACOAT mutant was complemented by TUP5. Two null alleles of TUP5 caused a reduced viability of gametes and embryo lethality, possibly caused by insufficient Arg supply from maternal tissue. TUP5 expression is positively regulated by light, and a TUP5-green fluorescent protein was localized in chloroplasts. tup5-1 has a unique light-dependent short root phenotype. Roots of light-grown tup5-1 seedlings switch from indeterminate growth to determinate growth with arresting cell production and an exhausted root apical meristem. The inhibitory activity was specific for blue light, and the inhibiting light was perceived by the root. Thus, tup5-1 reveals a novel role of amino acids and blue light in regulating root meristem function