Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Crop supply dynamics and the illusion of partial adjustment

We use field-level data to estimate the response of corn and soybean acreage to price shocks. Our sample contains more than eight million observations derived from satellite imagery and includes every field in Iowa, Illinois, and Indiana. We estimate that aggregate crop acreage responds more to price shocks in the short run than in the long run, and we show theoretically how the benefits of crop rotation generate this response pattern. In essence, farmers who change crops due to a price shock have an incentive to switch back to the previous crop to capture the benefits of crop rotation. Our result contradicts the long-held belief that agricultural supply responds gradually to price shocks through partial adjustment. We would not have obtained this result had we used county-level panel data. Standard econometric methods applied to county-level data produce estimates consistent with partial adjustment. We show that this apparent partial adjustment is illusory, and we demonstrate how it arises from the fact that fields in the same county are more similar to each other than to fields in other counties. This result underscores the importance of using models with appropriate micro-foundations and cautions against inferring micro-level rigidities from inertia in aggregate panel data. Our preferred estimate of the own-price long-run elasticity of corn acreage is 0.29 and the cross-price elasticity is -0.22. The corresponding elasticities for soybean acreage are 0.26 and -0.33. Our estimated short-run elasticities are 37 percent larger than their long-run counterparts

Identification of independent association signals and putative functional variants for breast cancer risk through fine-scale mapping of the 12p11 locus.

BACKGROUND: Multiple recent genome-wide association studies (GWAS) have identified a single nucleotide polymorphism (SNP), rs10771399, at 12p11 that is associated with breast cancer risk. METHOD: We performed a fine-scale mapping study of a 700 kb region including 441 genotyped and more than 1300 imputed genetic variants in 48,155 cases and 43,612 controls of European descent, 6269 cases and 6624 controls of East Asian descent and 1116 cases and 932 controls of African descent in the Breast Cancer Association Consortium (BCAC; http://bcac.ccge.medschl.cam.ac.uk/ ), and in 15,252 BRCA1 mutation carriers in the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA). Stepwise regression analyses were performed to identify independent association signals. Data from the Encyclopedia of DNA Elements project (ENCODE) and the Cancer Genome Atlas (TCGA) were used for functional annotation. RESULTS: Analysis of data from European descendants found evidence for four independent association signals at 12p11, represented by rs7297051 (odds ratio (OR) = 1.09, 95 % confidence interval (CI) = 1.06-1.12; P = 3 × 10(-9)), rs805510 (OR = 1.08, 95 % CI = 1.04-1.12, P = 2 × 10(-5)), and rs1871152 (OR = 1.04, 95 % CI = 1.02-1.06; P = 2 × 10(-4)) identified in the general populations, and rs113824616 (P = 7 × 10(-5)) identified in the meta-analysis of BCAC ER-negative cases and BRCA1 mutation carriers. SNPs rs7297051, rs805510 and rs113824616 were also associated with breast cancer risk at P < 0.05 in East Asians, but none of the associations were statistically significant in African descendants. Multiple candidate functional variants are located in putative enhancer sequences. Chromatin interaction data suggested that PTHLH was the likely target gene of these enhancers. Of the six variants with the strongest evidence of potential functionality, rs11049453 was statistically significantly associated with the expression of PTHLH and its nearby gene CCDC91 at P < 0.05. CONCLUSION: This study identified four independent association signals at 12p11 and revealed potentially functional variants, providing additional insights into the underlying biological mechanism(s) for the association observed between variants at 12p11 and breast cancer risk.UK funding includes Cancer Research UK and NIH.This is the final version of the article. It first appeared from BioMed Central via http://dx.doi.org/10.1186/s13058-016-0718-

A century of trends in adult human height

Being taller is associated with enhanced longevity, and higher education and earnings. We reanalysed 1472 population-based studies, with measurement of height on more than 18.6 million participants to estimate mean height for people born between 1896 and 1996 in 200 countries. The largest gain in adult height over the past century has occurred in South Korean women and Iranian men, who became 20.2 cm (95% credible interval 17.5-22.7) and 16.5 cm (13.3-19.7) taller, respectively. In contrast, there was little change in adult height in some sub-Saharan African countries and in South Asia over the century of analysis. The tallest people over these 100 years are men born in the Netherlands in the last quarter of 20th century, whose average heights surpassed 182.5 cm, and the shortest were women born in Guatemala in 1896 (140.3 cm; 135.8-144.8). The height differential between the tallest and shortest populations was 19-20 cm a century ago, and has remained the same for women and increased for men a century later despite substantial changes in the ranking of countries

Loving to Straighten Out Development: Sexuality and ‘Ethnodevelopment’ in the World Bank’s Ecuadorian Lending

Gender staff in the World Bank -- the world's largest and most influential development institution -- have a policy problem. Having prioritised efforts to get women into paid employment as the "cure-all" for gender inequality they must deal with the work that women already do -- the unpaid labour of caring, socialisation, and human needs fulfilment. This article explores the most prominent policy solution enacted by the Bank to this tension between paid and unpaid work: the restructuring of normative heterosexuality to encourage a two-partner model of love and labour wherein women work more and men care better. Through a case study of Bank gender lending in Ecuador I argue that staff are trying to (re)forge normative arrangements of intimacy, a policy preference that remains invisible unless sexuality is taken seriously as a category of analysis in development studies. Specifically, I focus on four themes that emerge from the attempt to restructure heteronormativity in the loan: (1) the definition of good gender analysis as requiring complementary sharing and dichotomous sex; (2) the Bank's attempt to inculcate limited rationality in women such that they operate as better workers while retaining altruistic attachments to loved ones; (3) the Bank's attempt to inculcate better loving in men, such that they pick up the slack of caring labour when their (partially) rational wives move into productive work, and; (4) the invocation of a racialised hierarchy resting on the extent to which communities approximate ideals of sharing monogamous partnership. Aside from providing clear evidence that the world's largest development institution is involved in micro-processes of sexuality adjustment alongside macro-processes of economic restructuring, I also critique the Bank's sexualised policy interventions and suggest that they warrant contestation

La conquista spagnola di Castelnuovo e l'assedio ottomano (1538-39): Gutierre de Cetina, Luigi Tansillo ed Hernando de Herrera: le armi e la poesia.

Alla conquista spagnola (1538) di Castelnuovo (Herceg Novi), l'Impero ottomano rispose con veemenza, riconquistando la citt\ue0 nel 1539. I soldati di Barbarossa passarone per le armi i 3000 soldati spagnoli della guarnigione. Il fatto provoc\uf2 grande emozione e fu celebrato dai poeti-soldato Luigi Tansillo e Gutierre de Cetina e dal poeta di mestiere Hernando de Herrera