Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

PAMELA results on the cosmic-ray antiproton flux from 60 MeV to 180 GeV in kinetic energy

The satellite-borne experiment PAMELA has been used to make a new measurement of the cosmic-ray antiproton flux and the antiproton-to-proton flux ratio which extends previously published measurements down to 60 MeV and up to 180 GeV in kinetic energy. During 850 days of data acquisition approximately 1500 antiprotons were observed. The measurements are consistent with purely secondary production of antiprotons in the galaxy. More precise secondary production models are required for a complete interpretation of the results.Comment: 11 pages, 3 figures, 1 table. Accepted for publication in Physical Review Letter

Density of Gr1-positive myeloid precursor cells, p-STAT3 expression and gene expression pattern in canine mammary cancer metastasis

The very recent studies on human and mice models have indicated an important role of myeloid precursor cells (progenitors or not fully differentiated cells that express the Gr1 antigen also called Gr1-positive myeloid suppressor cells) in the tumor progression and metastasis. They are thought to suppress the immune system and promote angiogenesis via Signal transducer and activator of transcription 3 (STAT3) activation. As of now there is no data available on the correlation of Gr1-positive cell number, phosphorylated STAT3 (p-STAT3) expression and cancer ability to metastasis. Thus, we counted the myeloid precursor cell number and analyzed p-STAT3 expression in 50 canine mammary tumors that gave local/distant metastases and did not metastasize. We showed that the number of Gr1-positive cells and p-STAT3 expression are significantly higher (p < 0.001) in the metastatic tumors than in the non-metastatic ones. We also observed higher expression of p-STAT3 in the canine mammary cancer cell lines with metastatic potential than in other cell lines (p < 0.001). Moreover, the number of myeloid precursors and p-STAT3 expression in metastatic tumors correlate strongly. The tumor infiltrating myeloid precursor cells may invigorate the STAT3 activity (probably via vascular endothelial growth factor – VEGF) that contributes to the tumor angiogenesis and furthermore tumor`s ability to metastasize. The analysis of gene expression in canine mammary cancer cell lines with metastatic potential indicated that semaphorin 3B (SEMA3B) and neuropilin receptors (NRP) may also be important elements in this process. Thus, we discuss the possible interactions within the tumor that may be required for cancer metastatis

A Novel, Low-Volume Method for Organ Culture of Embryonic Kidneys That Allows Development of Cortico-Medullary Anatomical Organization

Here, we present a novel method for culturing kidneys in low volumes of medium that offers more organotypic development compared to conventional methods. Organ culture is a powerful technique for studying renal development. It recapitulates many aspects of early development very well, but the established techniques have some disadvantages: in particular, they require relatively large volumes (1–3 mls) of culture medium, which can make high-throughput screens expensive, they require porous (filter) substrates which are difficult to modify chemically, and the organs produced do not achieve good cortico-medullary zonation. Here, we present a technique of growing kidney rudiments in very low volumes of medium–around 85 microliters–using silicone chambers. In this system, kidneys grow directly on glass, grow larger than in conventional culture and develop a clear anatomical cortico-medullary zonation with extended loops of Henle

The study of Priapulus caudatus reveals conserved molecular patterning underlying different gut morphogenesis in the Ecdysozoa

Background The digestive systems of animals can become highly specialized in response to their exploration and occupation of new ecological niches. Although studies on different animals have revealed commonalities in gut formation, the model systems Caenorhabditis elegans and Drosophila melanogaster, which belong to the invertebrate group Ecdysozoa, exhibit remarkable deviations in how their intestines develop. Their morphological and developmental idiosyncrasies have hindered reconstructions of ancestral gut characters for the Ecdysozoa, and limit comparisons with vertebrate models. In this respect, the phylogenetic position, and slow evolving morphological and molecular characters of marine priapulid worms advance them as a key group to decipher evolutionary events that occurred in the lineages leading to C. elegans and D. melanogaster. Results In the priapulid Priapulus caudatus, the gut consists of an ectodermal foregut and anus, and a mid region of at least partial endodermal origin. The inner gut develops into a 16-cell primordium devoid of visceral musculature, arranged in three mid tetrads and two posterior duplets. The mouth invaginates ventrally and shifts to a terminal anterior position as the ventral anterior ectoderm differentially proliferates. Contraction of the musculature occurs as the head region retracts into the trunk and resolves the definitive larval body plan. Despite obvious developmental differences with C. elegans and D. melanogaster, the expression in P. caudatus of the gut-related candidate genes NK2.1, foxQ2, FGF8/17/18, GATA456, HNF4, wnt1, and evx demonstrate three distinct evolutionarily conserved molecular profiles that correlate with morphologically identified sub-regions of the gut. Conclusions The comparative analysis of priapulid development suggests that a midgut formed by a single endodermal population of vegetal cells, a ventral mouth, and the blastoporal origin of the anus are ancestral features in the Ecdysozoa. Our molecular data on P. caudatus reveal a conserved ecdysozoan gut-patterning program and demonstrates that extreme morphological divergence has not been accompanied by major molecular innovations in transcriptional regulators during digestive system evolution in the Ecdysozoa. Our data help us understand the origins of the ecdysozoan body plan, including those of C. elegans and D. melanogaster, and this is critical for comparisons between these two prominent model systems and their vertebrate counterparts