Dirac-harmonic maps from index theory

We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the source and target manifolds is a harmonic map.Comment: 26 pages, no figur

Harmonic maps from degenerating Riemann surfaces

We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and $C^{0}$ modulo bubbles of sequences of such maps.Comment: 27 page

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

Assessment of pollen rewards by foraging bees

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.The removal of pollen by flower-visiting insects is costly to plants, not only in terms of production, but also via lost reproductive potential. Modern angiosperms have evolved various reward strategies to limit these costs, yet many plant species still offer pollen as a sole or major reward for pollinating insects. 2. The benefits plants gain by offering pollen as a reward for pollinating are defined by the behaviour of their pollinators, some of which feed on the pollen at the flower, while others collect pollen to provision offspring. 3. We explore how pollen impacts on the behaviour and foraging decisions of pollen-collecting bees, drawing comparisons with what is known for nectar rewards. This question is of particular interest since foraging bees typically do not ingest pollen during collection, meaning the sensory pathways involved in evaluating this resource are not immediately obvious. 4. Previous research focussed on whether foraging bees can determine the quality of pollen sources offered by different plant species, and attempted to infer the mechanisms underpinning such evaluations, mainly through observations of collection preferences in the field 5. More recent experimental research has started to focus on if pollen itself can mediate the detection of, and learning about, pollen sources and associated floral cues. 6. We review advancements in the understanding of how bees forage for pollen and respond to variation in pollen quality, and discuss future directions for studying how this ancestral floral food reward shapes the behaviour of pollinating insects

Separation of breast cancer and organ microenvironment transcriptomes in metastases

Background: The seed and soil hypothesis was proposed over a century ago to describe why cancer cells (seeds) grow in certain organs (soil). Since then, the genetic properties that define the cancer cells have been heavily investigated; however, genomic mediators within the organ microenvironment that mediate successful metastatic growth are less understood. These studies sought to identify cancer- and organ-specific genomic programs that mediate metastasis. Methods: In these studies, a set of 14 human breast cancer patient-derived xenograft (PDX) metastasis models was developed and then tested for metastatic tropism with two approaches: spontaneous metastases from mammary tumors and intravenous injection of PDX cells. The transcriptomes of the cancer cells when growing as tumors or metastases were separated from the transcriptomes of the microenvironment via species-specific separation of the genomes. Drug treatment of PDX spheroids was performed to determine if genes activated in metastases may identify targetable mediators of viability. Results: The experimental approaches that generated metastases in PDX models were identified. RNA sequencing of 134 tumors, metastases, and normal non-metastatic organs identified cancer- and organ-specific genomic properties that mediated metastasis. A common genomic response of the liver microenvironment was found to occur in reaction to the invading PDX cells. Genes within the cancer cells were found to be either transiently regulated by the microenvironment or permanently altered due to clonal selection of metastatic sublines. Gene Set Enrichment Analyses identified more than 400 gene signatures that were commonly activated in metastases across basal-like PDXs. A Src signaling signature was found to be extensively upregulated in metastases, and Src inhibitors were found to be cytotoxic to PDX spheroids. Conclusions: These studies identified that during the growth of breast cancer metastases, there were genomic changes that occurred within both the cancer cells and the organ microenvironment. We hypothesize that pathways upregulated in metastases are mediators of viability and that simultaneously targeting changes within different cancer cell pathways and/or different tissue compartments may be needed for inhibition of disease progression

Effective Theoretical Approach to Back Reaction of the Dynamical Casimir Effect in 1+1 Dimensions

We present an approach to studying the Casimir effects by means of the effective theory. An essential point of our approach is replacing the mirror separation into the size of space S^1 in the adiabatic approximation. It is natural to identify the size of space S^1 with the scale factor of the Robertson-Walker-type metric. This replacement simplifies the construction of a class of effective models to study the Casimir effects. To check the validity of this replacement we construct a model for a scalar field coupling to the two-dimensional gravity and calculate the Casimir effects by the effective action for the variable scale factor. Our effective action consists of the classical kinetic term of the mirror separation and the quantum correction derived by the path-integral method. The quantum correction naturally contains both the Casimir energy term and the back-reaction term of the dynamical Casimir effect, the latter of which is expressed by the conformal anomaly. The resultant effective action describes the dynamical vacuum pressure, i.e., the dynamical Casimir force. We confirm that the force depends on the relative velocity of the mirrors, and that it is always attractive and stronger than the static Casimir force within the adiabatic approximation.Comment: Published Version, 16 pages, LaTeX2e with graphics package, 1 figur

Probing the Environment with Galaxy Dynamics

I present various projects to study the halo dynamics of elliptical galaxies. This allows one to study the outer mass and orbital distributions of ellipticals in different environments, and the inner distributions of groups and clusters themselves.Comment: 5 pages, 2 figs, to appear in Proc. ESO Workshop, Groups of Galaxies in the Nearby Universe (5-9 Dec 2005), eds. I. Saviane, V. Ivanov & J. Borissova (Springer-Verlag