Bounds for graph regularity and removal lemmas

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemer\'edi's regularity lemma. In order to gain some control over irregular pairs, another regularity lemma, known as the strong regularity lemma, was developed by Alon, Fischer, Krivelevich, and Szegedy. For this lemma, we prove a lower bound of wowzer-type, which is one level higher in the Ackermann hierarchy than the tower function, on the number of parts in the strong regularity lemma, essentially matching the upper bound. On the other hand, for the induced graph removal lemma, the standard application of the strong regularity lemma, we find a different proof which yields a tower-type bound. We also discuss bounds on several related regularity lemmas, including the weak regularity lemma of Frieze and Kannan and the recently established regular approximation theorem. In particular, we show that a weak partition with approximation parameter \epsilon may require as many as 2^{\Omega(\epsilon^{-2})} parts. This is tight up to the implied constant and solves a problem studied by Lov\'asz and Szegedy.Comment: 62 page

The ecdysteroidome of Drosophila: influence of diet and development

Ecdysteroids are the hormones regulating development, physiology and fertility in arthropods, which synthesize them exclusively from dietary sterols. But how dietary sterol diversity influences the ecdysteroid profile, how animals ensure the production of desired hormones and whether there are functional differences between different ecdysteroids produced in vivo remains unknown. This is because currently there is no analytical technology for unbiased, comprehensive and quantitative assessment of the full complement of endogenous ecdysteroids. We developed a new LC-MS/MS method to screen the entire chemical space of ecdysteroid-related structures and to quantify known and newly discovered hormones and their catabolites. We quantified the ecdysteroidome in Drosophila melanogaster and investigated how the ecdysteroid profile varies with diet and development. We show that Drosophila can produce four different classes of ecdysteroids, which are obligatorily derived from four types of dietary sterol precursors. Drosophila makes makisterone A from plant sterols and epi-makisterone A from ergosterol, the major yeast sterol. However, they prefer to selectively utilize scarce ergosterol precursors to make a novel hormone 24,28-dehydromakisterone A and trace cholesterol to synthesize 20-hydroxyecdysone. Interestingly, epi-makisterone A supports only larval development, whereas all other ecdysteroids allow full adult development. We suggest that evolutionary pressure against producing epi-C-24 ecdysteroids might explain selective utilization of ergosterol precursors and the puzzling preference for cholesterol.Max Planck Geselleschaft, Deutsche Forschungsgemeinschaft (TRR 83, projects A17 and A19), European Molecular Biology Organization Long Term Fellowship, University Pierre and Marie Curie

Enhancing the utility of antroduodenal manometry in pediatric intestinal pseudo-obstruction

BACKGROUND: Antroduodenal manometry (ADM) and histopathology are currently employed to aid the diagnosis of pediatric intestinal pseudo-obstruction (PIPO). Limited data are available on the reliability of ADM analysis and its correlation with histopathology. We aimed to develop a protocol for enhanced analysis of ADM contractile patterns, including a scoring system, and explore whether this provided better correlation with histopathology. METHODS: Children referred with suspected PIPO between April 2012-December 2019 who underwent both ADM and full-thickness biopsies were included. ADM tracings were analyzed using both standard (conventional ADM) and novel (enhanced ADM) motility parameters. A novel ADM score (GLASS score) was generated based on the enhanced ADM analysis. Conventional and enhanced ADM analyses were then correlated with histopathology. RESULTS: Forty patients were included. Using conventional clinical criteria, 29 of these were diagnosed with PIPO and the other 11 with non-PIPO diagnoses. Twenty-three of the PIPO patients had abnormal histopathology: 6 myopathy, 4 neuropathy, 3 neuro-myopathy, and 10 non-specific changes. No agreement in diagnosis was found between conventional ADM analysis and histopathology (ϰ = 0.068; p = 0.197), whereas the latter significantly correlated with enhanced ADM analysis (ϰ = 0.191; p = 0.003). The enhanced ADM score was significantly higher in PIPO versus non-PIPO (16.0 vs. 8.0; p < 0.001). CONCLUSIONS: As opposed to conventional analysis protocols, the newly developed enhanced ADM analysis and associated score is not only able to discriminate between PIPO and non-PIPO patients, but also between distinct histopathological pathologies. Further studies are required to assess the utility of enhanced ADM analysis in larger populations

Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.Comment: 20 pages, 9 image

On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

Chromosphere of K giant stars Geometrical extent and spatial structure detection

We aim to constrain the geometrical extent of the chromosphere of non-binary K giant stars and detect any spatial structures in the chromosphere. We performed observations with the CHARA interferometer and the VEGA beam combiner at optical wavelengths. We observed seven non-binary K giant stars. We measured the ratio of the radii of the photosphere to the chromosphere using the interferometric measurements in the Halpha and the Ca II infrared triplet line cores. For beta Ceti, spectro-interferometric observations are compared to an non-local thermal equilibrium (NLTE) semi-empirical model atmosphere including a chromosphere. The NLTE computations provide line intensities and contribution functions that indicate the relative locations where the line cores are formed and can constrain the size of the limb-darkened disk of the stars with chromospheres. We measured the angular diameter of seven K giant stars and deduced their fundamental parameters: effective temperatures, radii, luminosities, and masses. We determined the geometrical extent of the chromosphere for four giant stars. The chromosphere extents obtained range between 16% to 47% of the stellar radius. The NLTE computations confirm that the Ca II/849 nm line core is deeper in the chromosphere of ? Cet than either of the Ca II/854 nm and Ca II/866 nm line cores. We present a modified version of a semi-empirical model atmosphere derived by fitting the Ca II triplet line cores of this star. In four of our targets, we also detect the signature of a differential signal showing the presence of asymmetries in the chromospheres. Conclusions. It is the first time that geometrical extents and structure in the chromospheres of non-binary K giant stars are determined by interferometry. These observations provide strong constrains on stellar atmosphere models.Comment: 10 pages, 12 figure

Exo-hydrogenated Single Wall Carbon Nanotubes

An extensive first-principles study of fully exo-hydrogenated zigzag (n,0) and armchair (n,n) single wall carbon nanotubes (C$_n$H$_n$), polyhedral molecules including cubane, dodecahedrane, and C$_{60}$H$_{60}$ points to crucial differences in the electronic and atomic structures relevant to hydrogen storage and device applications. C$_n$H$_n$'s are estimated to be stable up to the radius of a (8,8) nanotube, with binding energies proportional to 1/R. Attaching a single hydrogen to any nanotube is always exothermic. Hydrogenation of zigzag nanotubes is found to be more likely than armchair nanotubes with similar radius. Our findings may have important implications for selective functionalization and finding a way of separating similar radius nanotubes from each other.Comment: 5 pages, 4 postscript figures, Revtex file, To be appear in Physical Review

Disulfide-activated protein kinase G Iα regulates cardiac diastolic relaxation and fine-tunes the Frank-Starling response.

The Frank-Starling mechanism allows the amount of blood entering the heart from the veins to be precisely matched with the amount pumped out to the arterial circulation. As the heart fills with blood during diastole, the myocardium is stretched and oxidants are produced. Here we show that protein kinase G Iα (PKGIα) is oxidant-activated during stretch and this form of the kinase selectively phosphorylates cardiac phospholamban Ser16-a site important for diastolic relaxation. We find that hearts of Cys42Ser PKGIα knock-in (KI) mice, which are resistant to PKGIα oxidation, have diastolic dysfunction and a diminished ability to couple ventricular filling with cardiac output on a beat-to-beat basis. Intracellular calcium dynamics of ventricular myocytes isolated from KI hearts are altered in a manner consistent with impaired relaxation and contractile function. We conclude that oxidation of PKGIα during myocardial stretch is crucial for diastolic relaxation and fine-tunes the Frank-Starling response

Region of Excessive Flux of PeV Cosmic Rays in the Direction Toward Pulsars PSR J1840+5640 and LAT PSR J1836+5925

An analysis of arrival directions of extensive air showers (EAS) registered with the EAS MSU and EAS-1000 prototype arrays has revealed a region of excessive flux of PeV cosmic rays in the direction toward pulsars PSR J1840+5640 and LAT PSR J1836+5925 at significance level up to 4.5sigma. The first of the pulsars was discovered almost 30 years ago and is a well-studied old radio pulsar located at the distance of 1.7pc from the Solar system. The second pulsar belongs to a new type of pulsars, discovered by the space gamma-ray observatory Fermi, pulsations of which are not observed in optical and radio wavelengths but only in the gamma-ray range of energies (gamma-ray-only pulsars). In our opinion, the existence of the region of excessive flux of cosmic rays registered with two different arrays provides a strong evidence that isolated pulsars can give a noticeable contribution to the flux of Galactic cosmic rays in the PeV energy range.Comment: 14 pages; v.2: a few remarks to match a version accepted for Astronomy Letters added. They can be found by redefining the \NEW command in the preamble of the LaTeX fil

Influence of the Soret effect on convection of binary fluids

Convection in horizontal layers of binary fluids heated from below and in particular the influence of the Soret effect on the bifurcation properties of extended stationary and traveling patterns that occur for negative Soret coupling is investigated theoretically. The fixed points corresponding to these two convection structures are determined for realistic boundary conditions with a many mode Galerkin scheme for temperature and concentration and an accurate one mode truncation of the velocity field. This solution procedure yields the stable and unstable solutions for all stationary and traveling patterns so that complete phase diagrams for the different convection types in typical binary liquid mixtures can easily be computed. Also the transition from weakly to strongly nonlinear states can be analyzed in detail. An investigation of the concentration current and of the relevance of its constituents shows the way for a simplification of the mode representation of temperature and concentration field as well as for an analytically manageable few mode description.Comment: 30 pages, 12 figure