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We discuss the potential scattering on the noncompact star graph. The Schr\"{o}dinger operator with the short-range potential localizing in a neighborhood of the graph vertex is considered. We study the asymptotic behavior the corresponding scattering matrix in the zero-range limit. It has been known for a long time that in dimension 1 there is no non-trivial Hamiltonian with the distributional potential $\delta'$, i.e., the $\delta'$ potential acts as a totally reflecting wall. Several authors have, in recent years, studied the scattering properties of the regularizing potentials $\alpha\eps^{-2}Q(x/\eps)$ approximating the first derivative of the Dirac delta function. A non-zero transmission through the regularized potential has been shown to exist as $\eps\to0$. We extend these results to star graphs with the point interaction, which is an analogue of $\delta'$ potential on the line. We prove that generically such a potential on the graph is opaque. We also show that there exists a countable set of resonant intensities for which a partial transmission through the potential occurs. This set of resonances is referred to as the resonant set and is determined as the spectrum of an auxiliary Sturm-Liouville problem associated with $Q$ on the graph., Comment: 16 pages, 2 figures

Kras mutations in colorectal cancer (CRC) are associated with clinical resistance to treatment with the epidermal growth factor receptor (EGFR)-targeted monoclonal antibodies. It has been suggested that cancer stem cells drive tumor growth and progression and are preferentially resistant to many current therapies. Delta-like 4 ligand (DLL4) is an important component of the Notch signaling pathway which is known to mediate stem cell self-renewal and vascular development. We have recently demonstrated that inhibition of human DLL4 in the tumor reduced cancer stem cell frequency, whereas inhibition of mouse DLL4 resulted in hyperproliferation of the tumor vasculature (Cell Stem Cell, 5:168-177, 2009). The goal of the present study is to extend the utility of anti-DLL4 in treatment of mutant Kras CRC. Consistent with clinical findings, mutant Kras colorectal xenograft tumors were generally insensitive to EGFR-targeted monoclonal antibody cetuximab and addition of anti-DLL4 did not further enhance cetuximab-mediated anti-tumor effect. In contrast, anti-DLL4 plus irinotecan was equally efficacious against both wild type and mutant Kras colon tumors. Gene expression analysis showed that anti-DLL4 affected vascular-related genes in the stroma and Notch target genes in the tumor and stroma. Further analysis of mutant Kras tumors indicated that anti-DLL4/ irinotecan combination produced a 5-fold decrease in colon cancer stem cell frequency compared to control antibody treated group. In conclusion, our findings provide a rationale for targeting cancer stem cells and tumor vasculature through inhibition of the DLL4/Notch signaling for treatment of CRC patients with Kras mutation. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 4295.

1. Es werden zwei Herzen mit Pulmonalarterienatresie, Kammerseptumdefekt, reitender Aorta und verschlossenem Ductus arteriosus Botalli beschrieben, die von 11 Wochen bzw. 23 Jahre alten Individuen stammten. In beiden Fallen bestanden insofern seltene Anomalien, als die atretischen Pulmonalarterien ihr Blut aus den Koronararterien bezogen, zu denen jeweils eine breite Gefaskommunikation vorlag, und zwar im ersten Fall zum Ostium der rechten, im zweiten Fall zum Hauptstamm der linken Kranzader. Es war somit auf naturlichem Wege eine Arterialisation der Lunge gegeben, wie wir sie kunstlich durch dieBlalocksche Operationsmethode mittels Einpflanzung der Arteria subclavia in die Arteria pulmonalis zu erreichen suchen. 2. Der Entstehungsmodus dieses doppelten Ursprungs einer Kranzarterie aus beiden, dem pulmonalen und dem aortalen Sinus Valsalvae wird entwicklungsgeschichtlich gedeutet: die embryonale Anlage einer Koronararterienknospe im Truncus arteriosus communis des fetalen Herzens wird durch das auftreffende Septum aorto-pulmonale im Entwicklungsgang gespalten und die halbierten Endothelknospen werden somit beiden spateren Gefasrohren zugeordnet. Dadurch kann die deltaformige Verbindung einer Koronararterie zu den beiden Hauptherzgefasen — Aorta und Pulmonalis — entwicklungsgeschichtlich verstanden werden.

The DELTA robot and the manipulators derived from the DELTA robot are a relevant class of translational manipulators. In this paper the mobility analysis of these parallel translational manipulators is developed in full. The manufacturing and mounting conditions that guarantee the pure translation of the platform are analytically derived. Moreover, it is presented the demonstration that these manipulators can assume singular configurations, named rotation singularities, in which they are not able to impose the platform translation any longer. Finally, the geometric and analytic conditions that make it possible to find all the singular configurations of these manipulators are provided.Copyright © 2002 by ASME

Quantum dots semiconductor heterostructures exhibit optical and electronic properties similar to those of real atoms, due to the delta like dispersion of the density of states. The study of the optical and electronic properties of artificial atoms in high magnetic fields allows the observation of quantum effects typical of the atomic physics. In this work we review the problem of artificial atoms in magnetic fields starting from the single-particle theory up to the problems encountered in the observation of correlation effects when two or more carriers are confined in the dot. The main experiments elucidating the change of the optical and electronic properties of artifical atoms in magnetic fields are also reviewed.

Background Bergmann glia (BG) are unipolar cerebellar astrocytes. The somata of mature BG reside in the Purkinje cell layer and extend radially arranged processes to the pial surface. BG have multiple branched processes, which enwrap the synapses of Purkinje cell dendrites. They migrate from the ventricular zone and align next to the Purkinje cell layer during development. Previously, we reported that Notch1, Notch2, and RBPj genes in the BG play crucial roles in the monolayer formation and morphogenesis of BG. However, it remains to be determined which ligand activates Nocth1 and Notch 2 on BG. Delta-like 1 (Dll1) is a major ligand of Notch receptors that is expressed in the developing cerebellum. Results In this study, we used human glial fibrillary acidic protein (hGFAP) promoter-driven Cre-mediated recombination to delete Dll1 in BG. Dll1-conditional mutant mice showed disorganization of Bergmann fibers, ectopic localization of BG in the molecular layer and a reduction in the number of BG. Conclusion These results suggest that Dll1 is required for the formation of the BG layer and its morphological maturation, apparently through a Notch1/2-RBPj dependent signaling pathway.