On consecutive pattern-avoiding permutations of length 4, 5 and beyond

We review and extend what is known about the generating functions for consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their asymptotic behaviour. There are respectively, seven length-4 and twenty-five length-5 consecutive-Wilf classes. D-finite differential equations are known for the reciprocal of the exponential generating functions for four of the length-4 and eight of the length-5 classes. We give the solutions of some of these ODEs. An unsolved functional equation is known for one more class of length-4, length-5 and beyond. We give the solution of this functional equation, and use it to show that the solution is not D-finite. For three further length-5 c-Wilf classes we give recurrences for two and a differential-functional equation for a third. For a fourth class we find a new algebraic solution. We give a polynomial-time algorithm to generate the coefficients of the generating functions which is faster than existing algorithms, and use this to (a) calculate the asymptotics for all classes of length 4 and length 5 to significantly greater precision than previously, and (b) use these extended series to search, unsuccessfully, for D-finite solutions for the unsolved classes, leading us to conjecture that the solutions are not D-finite. We have also searched, unsuccessfully, for differentially algebraic solutions.Comment: 23 pages, 2 figures (update of references, plus web link to enumeration data). Minor update. Typos corrected. One additional referenc

The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics

Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \emph{$k$-sided prudent walks} (with $k=1,2,3,4$) are, in essence, only allowed to grow along $k$ directions. Prudent polygons are prudent walks that return to a point adjacent to their starting point. Prudent walks and polygons have been previously enumerated by length and perimeter (Bousquet-M\'elou, Schwerdtfeger; 2010). We consider the enumeration of \emph{prudent polygons} by \emph{area}. For the 3-sided variety, we find that the generating function is expressed in terms of a $q$-hypergeometric function, with an accumulation of poles towards the dominant singularity. This expression reveals an unusual asymptotic structure of the number of polygons of area $n$, where the critical exponent is the transcendental number $\log_23$ and and the amplitude involves tiny oscillations. Based on numerical data, we also expect similar phenomena to occur for 4-sided polygons. The asymptotic methodology involves an original combination of Mellin transform techniques and singularity analysis, which is of potential interest in a number of other asymptotic enumeration problems.Comment: 27 pages, 6 figure

Compressed self-avoiding walks, bridges and polygons

We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all vertices of maximal height. We first use the conjectured relation with the Schramm-Loewner evolution to predict the form of the partition function including the values of the exponents, and then we use series analysis to test these predictions.Comment: 29 pages, 6 figure

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

Handedness and behavioural inhibition system/behavioural activation system (BIS/BAS) scores: A replication and extension of Wright, Hardie, and Wilson (2009)

The Annett Hand Preference Questionnaire (AHPQ) as modified by Briggs and Nebes was administered along with Carver and White's behavioural inhibition system (BIS) and behavioural activation system (BAS) scale and a shortened form of the Big Five personality questionnaire to 92 university students. After eliminating the data from five respondents who reported having changed handedness and one outlier, there was a significant sex difference in mean BIS scores, with females (n = 43) scoring higher than males (n = 43). Replicating the results of Wright, Hardie and Wilson, non-right-handers (n = 36) had significantly higher mean BIS score than right-handers (n = 50). Controlling for sex of participant, neuroticism and BAS sub-scale scores in hierarchical regression analyses left this BIS effect substantially unaffected. There was no handedness or sex difference on any of the three BAS sub-scales. Further analyses revealed no association between strength, as distinct from direction, of handedness and BIS (or BAS) scores. The findings are discussed with reference to recent developments in reinforcement sensitivity theory on which BIS/BAS variables are based

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

Empirical 2MASS-WFC3/IR filter transformations from synthetic photometry

Near-infrared bandpasses on spaceborne observatories diverge from their ground-based counterparts as they are free of atmospheric telluric absorption. Available transformations between respective filter systems in the literature rely on theoretical stellar atmospheres, which are known to have difficulties reproducing observed spectral energy distributions of cool giants. We present new transformations between the 2MASS $JHK_S$ and HST WFC3/IR F110W, F125W, & F160W photometric systems based on synthetic photometry of empirical stellar spectra from four spectral libraries. This sample comprises over 1000 individual stars, which together span nearly the full HR diagram and sample stellar populations from the solar neighborhood out to the Magellanic Clouds, covering a broad range of ages, metallicities, and other relevant stellar properties. In addition to global color-dependent transformations, we examine band-to-band differences for cool, luminous giant stars in particular, including multiple types of primary distance indicators.Comment: 24 pages, 15 figures, accepted to A

Fractionating negative and positive affectivity in handedness: Insights from the Reinforcement Sensitivity Theory of personality

The Annett Hand Preference Questionnaire (AHPQ), as modified by Briggs and Nebes [(1975). Patterns of hand preference in a student population. Cortex, 11(3), 230-238. doi: 10.1016/s0010-9452(75)80005-0 ], was administered to a sample of 177 participants alongside the Reinforcement Sensitivity Theory of Personality Questionnaire [RST-PQ; Corr, P. J., & Cooper, A. (2016). The Reinforcement Sensitivity Theory of Personality Questionnaire (RST-PQ): Development and validation. Psychological Assessment. doi: 10.1037/pas000 ], which measures two factors of defensive negative emotion, motivation and affectivity-the Behavioural Inhibition System (BIS) and the Fight-Flight-Freeze System (FFFS)-and one positive-approach dimension related to reward sensitivity, persistence and reactivity-the Behavioural Approach System. We sought to clarify the nature of negative, and positive, affectivity in relation to handedness. ANOVAs and multiple regression analyses converged on the following conclusions: left-handers were higher on the BIS, not the FFFS, than right-handers; in right-handers only, strength of hand preference was positively correlated with the FFFS, not the BIS. The original assessment method proposed by Annett was also used to assess handedness, but associations with RST-PQ factors were not found. These findings help us to clarify existing issues in the literature and raise new ones for future research

Final targeting strategy for the sloan digital sky survey IV Apache Point Observatory galactic evolution experiment 2 North Survey

Artículo escrito por más de 60 autores.The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is a dual-hemisphere, near-infrared (NIR), spectroscopic survey with the goal of producing a chemodynamical mapping of the Milky Way. The targeting for APOGEE-2 is complex and has evolved with time. In this paper, we present the updates and additions to the initial targeting strategy for APOGEE-2N presented in Zasowski et al. (2017). These modifications come in two implementation modes: (i) “Ancillary Science Programs” competitively awarded to Sloan Digital Sky Survey IV PIs through proposal calls in 2015 and 2017 for the pursuit of new scientific avenues outside the main survey, and (ii) an effective 1.5 yr expansion of the survey, known as the Bright Time Extension (BTX), made posible through accrued efficiency gains over the first years of the APOGEE-2N project. For the 23 distinct ancillary programs, we provide descriptions of the scientific aims, target selection, and how to identify these targets within the APOGEE-2 sample. The BTX permitted changes to the main survey strategy, the inclusion of new programs in response to scientific discoveries or to exploit major new data sets not available at the outset of the survey design, and expansions of existing programs to enhance their scientific success and reach. After describing the motivations, implementation, and assessment of these programs, we also leave a summary of lessons learned from nearly a decade of APOGEE-1 and APOGEE-2 survey operations. A companion paper, F. Santana et al. (submitted; AAS29036), provides a complementary presentation of targeting modifications relevant to APOGEE-2 operations in the Southern Hemisphere