A unified approach on Springer fibers in the hook, two-row and two-column cases

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan basis and consider the standard torus relative to this. We deal with the problem to describe the flags fixed by the torus which belong to a given component of the Springer fiber. We solve the problem in the hook, two-row and two-column cases. We provide two main characterizations which are common to the three cases, and which involve dominance relations between Young diagrams and combinatorial algorithms. Then, for these three cases, we deduce topological properties of the components and their intersections.Comment: 42 page

A risk prediction model for the assessment and triage of women with hypertensive disorders of pregnancy in low-resourced settings: the miniPIERS (Pre-eclampsia Integrated Estimate of RiSk) multi-country prospective cohort study.

BACKGROUND: Pre-eclampsia/eclampsia are leading causes of maternal mortality and morbidity, particularly in low- and middle- income countries (LMICs). We developed the miniPIERS risk prediction model to provide a simple, evidence-based tool to identify pregnant women in LMICs at increased risk of death or major hypertensive-related complications. METHODS AND FINDINGS: From 1 July 2008 to 31 March 2012, in five LMICs, data were collected prospectively on 2,081 women with any hypertensive disorder of pregnancy admitted to a participating centre. Candidate predictors collected within 24 hours of admission were entered into a step-wise backward elimination logistic regression model to predict a composite adverse maternal outcome within 48 hours of admission. Model internal validation was accomplished by bootstrapping and external validation was completed using data from 1,300 women in the Pre-eclampsia Integrated Estimate of RiSk (fullPIERS) dataset. Predictive performance was assessed for calibration, discrimination, and stratification capacity. The final miniPIERS model included: parity (nulliparous versus multiparous); gestational age on admission; headache/visual disturbances; chest pain/dyspnoea; vaginal bleeding with abdominal pain; systolic blood pressure; and dipstick proteinuria. The miniPIERS model was well-calibrated and had an area under the receiver operating characteristic curve (AUC ROC) of 0.768 (95% CI 0.735-0.801) with an average optimism of 0.037. External validation AUC ROC was 0.713 (95% CI 0.658-0.768). A predicted probability ≥25% to define a positive test classified women with 85.5% accuracy. Limitations of this study include the composite outcome and the broad inclusion criteria of any hypertensive disorder of pregnancy. This broad approach was used to optimize model generalizability. CONCLUSIONS: The miniPIERS model shows reasonable ability to identify women at increased risk of adverse maternal outcomes associated with the hypertensive disorders of pregnancy. It could be used in LMICs to identify women who would benefit most from interventions such as magnesium sulphate, antihypertensives, or transportation to a higher level of care

Anomaly Equations and Intersection Theory

Six-dimensional supergravity theories with N=(1,0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional N=(1,0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric counterpart of the anomaly coefficients---in particular, those of the abelian gauge groups---that govern the low-energy dynamics of the theory. We discuss the results in the context of investigating string universality in six dimensions.Comment: 29 pages + appendices, 8 figures; v2: minor corrections, references added; v3: minor corrections, reference adde

From counting to construction of BPS states in N=4 SYM

We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry group. A related projector acting on the Hilbert space of the free theory is used to construct the matrix of two-point functions of the states annihilated by the one-loop dilatation operator, at finite N or in the large N limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of symmetric groups and dimensions of U(N) representations. It is expected, by non-renormalization theorems, to contain observables at strong coupling. Using the stringy exclusion principle, we interpret a class of its eigenvalues and eigenvectors in terms of giant gravitons. We also give a formula for the action of the one-loop dilatation operator on the orthogonal basis of the free theory, which is manifestly covariant under the global symmetry.Comment: 41 pages + Appendices, 4 figures; v2 - refs and acknowledgments adde

Genetic variation in the Solanaceae fruit bearing species lulo and tree tomato revealed by Conserved Ortholog (COSII) markers

The Lulo or naranjilla (Solanum quitoense Lam.) and the tree tomato or tamarillo (Solanum betaceum Cav. Sendt.) are both Andean tropical fruit species with high nutritional value and the potential for becoming premium products in local and export markets. Herein, we present a report on the genetic characterization of 62 accessions of lulos (n = 32) and tree tomatoes (n = 30) through the use of PCR-based markers developed from single-copy conserved orthologous genes (COSII) in other Solanaceae (Asterid) species. We successfully PCR amplified a set of these markers for lulos (34 out of 46 initially tested) and tree tomatoes (26 out of 41) for molecular studies. Six polymorphic COSII markers were found in lulo with a total of 47 alleles and five polymorphic markers in tree tomato with a total of 39 alleles in the two populations. Further genetic analyses indicated a high population structure (with FST > 0.90), which may be a result of low migration between populations, adaptation to various niches and the number of markers evaluated. We propose COSII markers as sound tools for molecular studies, conservation and the breeding of these two fruit species

Emergent global patterns of ecosystem structure and function from a mechanistic general ecosystem model

Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model (GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments. Functional forms and parameter values were derived from the theoretical and empirical literature where possible. Simulations of the fate of all organisms with body masses between 10 µg and 150,000 kg (a range of 14 orders of magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in general agreement with current data and theory. These properties emerged from our encoding of the biology of, and interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures

A rocky composition for an Earth-sized exoplanet

Planets with sizes between that of Earth (with radius R[subscript circle in cross]) and Neptune (about 4 R[subscript circle in cross]) are now known to be common around Sun-like stars. Most such planets have been discovered through the transit technique, by which the planet’s size can be determined from the fraction of starlight blocked by the planet as it passes in front of its star. Measuring the planet’s mass—and hence its density, which is a clue to its composition—is more difficult. Planets of size 2–4 R[subscript circle in cross] have proved to have a wide range of densities, implying a diversity of compositions, but these measurements did not extend to planets as small as Earth. Here we report Doppler spectroscopic measurements of the mass of the Earth-sized planet Kepler-78b, which orbits its host star every 8.5 hours (ref. 6). Given a radius of 1.20 ± 0.09 R[subscript circle in cross] and a mass of 1.69 ± 0.41 M[subscript circle in cross], the planet’s mean density of 5.3 ± 1.8 g cm[superscript −3] is similar to Earth’s, suggesting a composition of rock and iron.Kepler Participating Scientist Progra

The descriptive content of names as predicate modifiers

In this paper I argue that descriptive content associated with a proper name can serve as a truth-conditionally relevant adjunct and be an additional contribution of the name to the truth-conditions. Definite descriptions the so-and-so associated by speakers with a proper name can be used as qualifying prepositional phrases as so-and-so, so sentences containing a proper name NN is doing something could be understood as NN is doing something as NN (which means as so-and-so). Used as an adjunct, the descriptive content of a proper name expresses the additional circumstances of an action (a manner, reason, goal, time or purpose) and constitute a part of a predicate. I argue that qualifying prepositional phrases should be analyzed as predicate modifiers and propose a formal representation of modified predicates. The additional truth-conditional relevance of the descriptive content of a proper name helps to explain the phenomenon of the substitution failure of coreferential names in simple sentences

Strict evolutionary conservation followed rapid gene loss on human and rhesus Y chromosomes

The human X and Y chromosomes evolved from an ordinary pair of autosomes during the past 200–300 million years[superscript 1, 2, 3]. The human MSY (male-specific region of Y chromosome) retains only three percent of the ancestral autosomes’ genes owing to genetic decay[superscript 4, 5]. This evolutionary decay was driven by a series of five ‘stratification’ events. Each event suppressed X–Y crossing over within a chromosome segment or ‘stratum’, incorporated that segment into the MSY and subjected its genes to the erosive forces that attend the absence of crossing over[superscript 2, 6]. The last of these events occurred 30 million years ago, 5 million years before the human and Old World monkey lineages diverged. Although speculation abounds regarding ongoing decay and looming extinction of the human Y chromosome[superscript 7, 8, 9, 10], remarkably little is known about how many MSY genes were lost in the human lineage in the 25 million years that have followed its separation from the Old World monkey lineage. To investigate this question, we sequenced the MSY of the rhesus macaque, an Old World monkey, and compared it to the human MSY. We discovered that during the last 25 million years MSY gene loss in the human lineage was limited to the youngest stratum (stratum 5), which comprises three percent of the human MSY. In the older strata, which collectively comprise the bulk of the human MSY, gene loss evidently ceased more than 25 million years ago. Likewise, the rhesus MSY has not lost any older genes (from strata 1–4) during the past 25 million years, despite its major structural differences to the human MSY. The rhesus MSY is simpler, with few amplified gene families or palindromes that might enable intrachromosomal recombination and repair. We present an empirical reconstruction of human MSY evolution in which each stratum transitioned from rapid, exponential loss of ancestral genes to strict conservation through purifying selection