The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

Spherical geometry and integrable systems

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.Comment: 15 pages, 5 figure

Mid-infrared two photon absorption sensitivity of commercial detectors

We report on broad-band two-photon absorption (TPA) in several commercially available MIR inter-band bulk semiconductor photodetectors with the spectral cutoff in the range of 4.5–6 μm. The highest TPA responsivity of 2x10‾⁵ A−mm²/W² is measured for a nitrogen-cooled InSb photovoltaic detector. Its performance as a two-photon detector is validated by measuring the secondorder interferometric autocorrelation function of a multimode quantum cascade laser emitting at the wavelength of 8 μm

Expression of TRPC6 channels in human epithelial breast cancer cells

<p>Abstract</p> <p>Background</p> <p>TRP channels have been shown to be involved in tumour generation and malignant growth. However, the expression of these channels in breast cancer remains unclear. Here we studied the expression and function of endogenous TRPC6 channels in a breast cancer cell line (MCF-7), a human breast cancer epithelial primary culture (hBCE) and in normal and tumour breast tissues.</p> <p>Methods</p> <p>Molecular (Western blot and RT-PCR), and immunohistochemical techniques were used to investigate TRPC6 expression. To investigate the channel activity in both MCF-7 cells and hBCE we used electrophysiological technique (whole cell patch clamp configuration).</p> <p>Results</p> <p>A non selective cationic current was activated by the oleoyl-2-acetyl-sn-glycerol (OAG) in both hBCE and MCF-7 cells. OAG-inward current was inhibited by 2-APB, SK&F 96365 and La³⁺. TRPC6, but not TRPC7, was expressed both in hBCE and in MCF-7 cells. TRPC3 was only expressed in hBCE. Clinically, TRPC6 mRNA and protein were elevated in breast carcinoma specimens in comparison to normal breast tissue. Furthermore, we found that the overexpression of TRPC6 protein levels were not correlated with tumour grades, estrogen receptor expression or lymph node positive tumours.</p> <p>Conclusion</p> <p>Our results indicate that TRPC6 channels are strongly expressed and functional in breast cancer epithelial cells. Moreover, the overexpression of these channels appears without any correlation with tumour grade, ER expression and lymph node metastasis. Our findings support the idea that TRPC6 may have a role in breast carcinogenesis.</p

Light-Dependant Biostabilisation of Sediments by Stromatolite Assemblages

For the first time we have investigated the natural ecosystem engineering capacity of stromatolitic microbial assemblages. Stromatolites are laminated sedimentary structures formed by microbial activity and are considered to have dominated the shallows of the Precambrian oceans. Their fossilised remains are the most ancient unambiguous record of early life on earth. Stromatolites can therefore be considered as the first recognisable ecosystems on the planet. However, while many discussions have taken place over their structure and form, we have very little information on their functional ecology and how such assemblages persisted despite strong eternal forcing from wind and waves. The capture and binding of sediment is clearly a critical feature for the formation and persistence of stromatolite assemblages. Here, we investigated the ecosystem engineering capacity of stromatolitic microbial assemblages with respect to their ability to stabilise sediment using material from one of the few remaining living stromatolite systems (Highborne Cay, Bahamas). It was shown that the most effective assemblages could produce a rapid (12–24 h) and significant increase in sediment stability that continued in a linear fashion over the period of the experimentation (228 h). Importantly, it was also found that light was required for the assemblages to produce this stabilisation effect and that removal of assemblage into darkness could lead to a partial reversal of the stabilisation. This was attributed to the breakdown of extracellular polymeric substances under anaerobic conditions. These data were supported by microelectrode profiling of oxygen and calcium. The structure of the assemblages as they formed was visualised by low-temperature scanning electron microscopy and confocal laser microscopy. These results have implications for the understanding of early stromatolite development and highlight the potential importance of the evolution of photosynthesis in the mat forming process. The evolution of photosynthesis may have provided an important advance for the niche construction activity of microbial systems and the formation and persistence of the stromatolites which came to dominate shallow coastal environments for 80% of the biotic history of the earth

The origin of multicellularity in cyanobacteria

Background: Cyanobacteria are one of the oldest and morphologically most diverse prokaryotic phyla on our planet. The early development of an oxygen-containing atmosphere approximately 2.45 - 2.22 billion years ago is attributed to the photosynthetic activity of cyanobacteria. Furthermore, they are one of the few prokaryotic phyla where multicellularity has evolved. Understanding when and how multicellularity evolved in these ancient organisms would provide fundamental information on the early history of life and further our knowledge of complex life forms. Results: We conducted and compared phylogenetic analyses of 16S rDNA sequences from a large sample of taxa representing the morphological and genetic diversity of cyanobacteria. We reconstructed ancestral character states on 10,000 phylogenetic trees. The results suggest that the majority of extant cyanobacteria descend from multicellular ancestors. Reversals to unicellularity occurred at least 5 times. Multicellularity was established again at least once within a single-celled clade. Comparison to the fossil record supports an early origin of multicellularity, possibly as early as the “Great Oxygenation Event” that occurred 2.45 - 2.22 billion years ago. Conclusions: The results indicate that a multicellular morphotype evolved early in the cyanobacterial lineage and was regained at least once after a previous loss. Most of the morphological diversity exhibited in cyanobacteria today —including the majority of single-celled species— arose from ancient multicellular lineages. Multicellularity could have conferred a considerable advantage for exploring new niches and hence facilitated the diversification of new lineages

Molecular mechanisms of EGF signaling-dependent regulation of pipe, a gene crucial for dorsoventral axis formation in Drosophila

During Drosophila oogenesis the expression of the sulfotransferase Pipe in ventral follicle cells is crucial for dorsoventral axis formation. Pipe modifies proteins that are incorporated in the ventral eggshell and activate Toll signaling which in turn initiates embryonic dorsoventral patterning. Ventral pipe expression is the result of an oocyte-derived EGF signal which down-regulates pipe in dorsal follicle cells. The analysis of mutant follicle cell clones reveals that none of the transcription factors known to act downstream of EGF signaling in Drosophila is required or sufficient for pipe regulation. However, the pipe cis-regulatory region harbors a 31-bp element which is essential for pipe repression, and ovarian extracts contain a protein that binds this element. Thus, EGF signaling does not act by down-regulating an activator of pipe as previously suggested but rather by activating a repressor. Surprisingly, this repressor acts independent of the common co-repressors Groucho or CtBP

Space Telescope and Optical Reverberation Mapping Project. IX. Velocity–Delay Maps for Broad Emission Lines in NGC 5548

In this contribution, we achieve the primary goal of the active galactic nucleus (AGN) STORM campaign by recovering velocity–delay maps for the prominent broad emission lines (Lyα, C iv, He ii, and Hβ) in the spectrum of NGC 5548. These are the most detailed velocity–delay maps ever obtained for an AGN, providing unprecedented information on the geometry, ionization structure, and kinematics of the broad-line region. Virial envelopes enclosing the emission-line responses show that the reverberating gas is bound to the black hole. A stratified ionization structure is evident. The He ii response inside 5–10 lt-day has a broad single-peaked velocity profile. The Lyα, C iv, and Hβ responses extend from inside 2 to outside 20 lt-day, with double peaks at ±2500 km s−1 in the 10–20 lt-day delay range. An incomplete ellipse in the velocity–delay plane is evident in Hβ. We interpret the maps in terms of a Keplerian disk with a well-defined outer rim at R = 20 lt-day. The far-side response is weaker than that from the near side. The line-center delay $\tau =(R/c)(1-\sin i)\approx 5$ days gives the inclination i ≈ 45°. The inferred black hole mass is MBH ≈ 7 × 107 M⊙. In addition to reverberations, the fit residuals confirm that emission-line fluxes are depressed during the "BLR Holiday" identified in previous work. Moreover, a helical "Barber-Pole" pattern, with stripes moving from red to blue across the C iv and Lyα line profiles, suggests azimuthal structure rotating with a 2 yr period that may represent precession or orbital motion of inner-disk structures casting shadows on the emission-line region farther out