Slicings of parallelogram polyominoes: Catalan, schröder, baxter, and other sequences

We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, a new Schröder subset of Baxter permutations, and a new Schröder subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the m-skinny slicings and the m-rowrestricted slicings, for m ∈ N. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any m

Diagnosis and outcome of oesophageal Crohn's disease

BACKGROUND AND AIMS: Crohn's disease (CD) can involve any part of the gastrointestinal tract. We aimed to characterize clinical, endoscopic, histologic features and treatment outcomes of CD patients with oesophageal involvement. METHODS: We collected cases through a retrospective multicentre European Crohn's and Colitis Organisation CONFER [COllaborative Network For Exceptionally Rare case reports] project. Clinical data were recorded in a standardized case report form. RESULTS: A total of 40 patients were reported [22 males, mean (±SD, range) age at oesophageal CD diagnosis: 25 (±13.3, 10-71) years and mean time of follow-up: 67 (±68.1, 3-240) months]. Oesophageal involvement was established at CD diagnosis in 26 patients (65%) and during follow-up in 14. CD was exclusively located in the oesophagus in 2 patients. Thirteen patients (32.2%) were asymptomatic at oesophageal disease diagnosis. Oesophageal strictures were present in 5 patients and fistulizing oesophageal disease in one. Eight patients exhibited granulomas on biopsies. Proton-pump inhibitors (PPIs) were administered in 37 patients (92.5%). Three patients underwent endoscopic dilation for symptomatic strictures and none oesophageal-related surgery. Diagnosis in pre-established CD resulted in treatment modifications in 9/14 patients. Clinical remission of oesophageal disease was seen in 33/40 patients (82.5%) after a mean time of 7 (±5.6, 1-18) months. Follow-up endoscopy was performed in 29/40 patients and 26/29 (89.7%) achieved mucosal healing. CONCLUSION: In this case series the endoscopic and histologic characteristics of isolated oesophageal CD were similar to those reported in other sites of involvement. Treatment was primarily conservative, with PPIs administered in the majority of patients and modifications in pre-existing IBD-related therapy occurring in two thirds of them. Clinical and endoscopic remission was achieved in more than 80% of the patients.info:eu-repo/semantics/publishedVersio

Global Properties of M31's Stellar Halo from the SPLASH Survey: III. Measuring the Stellar Velocity Dispersion Profile

We present the velocity dispersion of red giant branch (RGB) stars in M31's halo, derived by modeling the line of sight velocity distribution of over 5000 stars in 50 fields spread throughout M31's stellar halo. The dataset was obtained as part of the SPLASH (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo) Survey, and covers projected radii of 9 to 175 kpc from M31's center. All major structural components along the line of sight in both the Milky Way (MW) and M31 are incorporated in a Gaussian Mixture Model, including all previously identified M31 tidal debris features in the observed fields. The probability an individual star is a constituent of M31 or the MW, based on a set of empirical photometric and spectroscopic diagnostics, is included as a prior probability in the mixture model. The velocity dispersion of stars in M31's halo is found to decrease only mildly with projected radius, from 108 km/s in the innermost radial bin (8.2 to 14.1 kpc) to $\sim 80$ to 90 km/s at projected radii of $\sim 40$ to 130 kpc, and can be parameterized with a power-law of slope $-0.12\pm 0.05$. The quoted uncertainty on the power-law slope reflects only the precision of the method, although other sources of uncertainty we consider contribute negligibly to the overall error budget.Comment: Submitted to the Astrophysical Journa

A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed on the honeycomb lattice persist on other lattices. This permits the accurate estimation, though not an exact evaluation, of certain critical amplitudes, as well as critical points, for these lattices. For the honeycomb lattice an exact amplitude for loops is proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis, giving greater precision. Explanation of why we observe what we do. Extra reference

Two-dimensional self-avoiding walks and polymer adsorption: Critical fugacity estimates

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is $1+\sqrt{2}$. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks interacting with a surface on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed for the honeycomb lattice persist irrespective of lattice. This permits the accurate estimation of the critical fugacity for the corresponding problem for the square and triangular lattices. We consider both edge and site weighting, and results of unprecedented precision are achieved. We also \emph{prove} the corresponding result fo the edge-weighted case for the honeycomb lattice.Comment: 12 pages, 3 figures, 7 table

Elemental Abundances in M31: Iron and Alpha Element Abundances in M31’s Outer Halo

We present [Fe/H] and [α/Fe] abundances, derived using spectral synthesis techniques, for stars in M31's outer stellar halo. The 21 [Fe/H] measurements and 7 [α/Fe] measurements are drawn from fields ranging from 43 to 165 kpc in projected distance from M31. We combine our measurements with existing literature measurements, and compare the resulting sample of 23 stars with [Fe/H] and 9 stars with [α/Fe] measurements in M31's outer halo with [α/Fe] and [Fe/H] measurements, also derived from spectral synthesis, in M31's inner stellar halo (r < 26 kpc) and dSph galaxies. The stars in M31's outer halo have [α/Fe] patterns that are consistent with the largest of M31's dSph satellites (And I and And VII). These abundances provide tentative evidence that the [α/Fe] abundances of stars in M31's outer halo are more similar to the abundances of Milky Way halo stars than to the abundances of stars in M31's inner halo. We also compare the spectral synthesis–based [Fe/H] measurements of stars in M31's halo with previous photometric [Fe/H] estimates, as a function of projected distance from M31. The spectral synthesis–based [Fe/H] measurements are consistent with a large-scale metallicity gradient previously observed in M31's stellar halo to projected distances as large as 100 kpc

Elemental Abundances in M31: The Kinematics and Chemical Evolution of Dwarf Spheroidal Satellite Galaxies

We present deep spectroscopy from Keck/DEIMOS of Andromeda I, III, V, VII, and X, all of which are dwarf spheroidal satellites of M31. The sample includes 256 spectroscopic members across all five dSphs. We confirm previous measurements of the velocity dispersions and dynamical masses, and we provide upper limits on bulk rotation. Our measurements confirm that M31 satellites obey the same relation between stellar mass and stellar metallicity as Milky Way (MW) satellites and other dwarf galaxies in the Local Group. The metallicity distributions show trends with stellar mass that are similar to those of MW satellites, including evidence in massive satellites for external influence, like pre-enrichment or gas accretion. We present the first measurements of individual element ratios, like [Si/Fe], in the M31 system, as well as measurements of the average [α/Fe] ratio. The trends of [α/Fe] with [Fe/H] also follow the same galaxy mass–dependent patterns as MW satellites. Less massive galaxies have more steeply declining slopes of [α/Fe] that begin at lower [Fe/H]. Finally, we compare the chemical evolution of M31 satellites to M31's Giant Stellar Stream and smooth halo. The properties of the M31 system support the theoretical prediction that the inner halo is composed primarily of massive galaxies that were accreted early. As a result, the inner halo exhibits higher [Fe/H] and [α/Fe] than surviving satellite galaxies

Elemental Abundances in M31: Iron and Alpha Element Abundances in M31's Outer Halo

We present [Fe/H] and [$\alpha$/Fe] abundances, derived using spectral synthesis techniques, for stars in M31's outer stellar halo. The 21 [Fe/H] measurements and 7 [$\alpha$/Fe] measurements are drawn from fields ranging from 43 to 165 kpc in projected distance from M31. We combine our measurements with existing literature measurements, and compare the resulting sample of 23 stars with [Fe/H] and 9 stars with [$\alpha$/Fe] measurements in M31's outer halo with [$\alpha$/Fe] and [Fe/H] measurements, also derived from spectral synthesis, in M31's inner stellar halo ($r <$26 kpc) and dSph galaxies. The stars in M31's outer halo have [$\alpha$/Fe] patterns that are consistent with the largest of M31's dSph satellites (And I and And VII). These abundances provide tentative evidence that the [$\alpha$/Fe] abundances of stars in M31's outer halo are more similar to the abundances of Milky Way halo stars than to the abundances of stars in M31's inner halo. We also compare the spectral synthesis-based [Fe/H] measurements of stars in M31's halo with previous photometric [Fe/H] estimates, as a function of projected distance from M31. The spectral synthesis-based [Fe/H] measurements are consistent with a large-scale metallicity gradient previously observed in M31's stellar halo to projected distances as large as 100 kpc.Comment: 18 pages, 9 figures, 1 table; accepted for publication in The Astronomical Journa