Distribution of periodic points of polynomial diffeomorphisms of C^2

This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of potential theory is the equilibrium measure $\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $\mu$ as the limit distribution of the periodic points of $f$

Comparative aspects of phytase and xylanase effects on performance, mineral digestibility, and ileal phytate degradation in broilers and turkeys

Two experiments were performed, using broilers or turkeys, each utilizing a 3 × 2 factorial arrangement, to compare their response to phytase and xylanase supplementation with growth performance, nutrient digestibility, and ileal phytate degradation as response criteria. For both experiments, 960 Ross 308 or 960 BUT 10 (0-day-old) birds were allocated to 6 treatments: (1) control diet, containing phytase at 500 FTU/kg; (2) the control diet with xylanase (16,000 BXU/kg); (3) the control diet supplemented on top with phytase (1,500 FTU/kg); (4) diet supplemented with 1,500 FTU/kg phytase and xylanase (16,000 BXU/kg); (5) the control diet supplemented with phytase (3,000 FTU/kg); and (6) diet supplemented with 3,000 FTU/kg phytase and xylanase (16,000 BXU/kg). Each treatment had 8 replicates of 20 birds each. Water and diets based on wheat, soybean meal, oilseed rape meal, and barley were available ad libitum. Body weight gain and feed intake were measured from 0 to 28 D, and feed conversion ratio (FCR) corrected for mortality was calculated. Ileal digestibility for dry matter and minerals on day 7 and 28 were analyzed in addition to levels of inositol phosphate esters (InsP6-3) and myo-inositol. Statistical comparisons were performed using ANOVA. Xylanase supplementation improved 28D FCR in broilers and turkeys. Increasing doses of phytase reduced FI and improved FCR only in broilers. In broilers, the age × phytase interaction for phosphorous digestibility showed that increasing phytase dose was more visible on day 7, than on day 28. Mineral digestibility was lower in 28-day-old turkey compared with 7-day-old turkey. InsP6 disappearance increased with increasing phytase levels in both species, with lower levels analyzed in turkeys. InsP6 disappearance was greater in younger turkeys (day 7 compared with day 28). In conclusion, although broilers and turkeys shared several similarities in their growth and nutrient utilization responses, the outcomes of the 2 trials also differed in many aspects. Whether this is because of difference in diets (InsP or Ca level) or differences between species needs further investigation

Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ coincides with the closure of the set of saddle points. The methods used combine the pluripotential theory with the theory of non-uniformly hyperbolic dynamical systems

Consistency Conditions on S-Matrix of Spin 1 Massless Particles

Motivated by new techniques in the computation of scattering amplitudes of massless particles in four dimensions, like BCFW recursion relations, the question of how much structure of the S-matrix can be determined from purely S-matrix arguments has received new attention. The BCFW recursion relations for massless particles of spin 1 and 2 imply that the whole tree-level S-matrix can be determined in terms of three-particle amplitudes (evaluated at complex momenta). However, the known proofs of the validity of the relations rely on the Lagrangian of the theory, either by using Feynman diagrams explicitly or by studying the effective theory at large complex momenta. This means that a purely S-matrix theoretic proof of the relations is still missing. The aim of this paper is to provide such a proof for spin 1 particles by extending the four-particle test introduced by P. Benincasa and F. Cachazo in arXiv:0705.4305[hep-th] to all particles. We show how n-particle tests imply that the rational function built from the BCFW recursion relations possesses all the correct factorization channels including holomorphic and anti-holomorphic collinear limits. This in turn implies that they give the correct S-matrix of the theory.Comment: 24 pages, 4 figure

Failure to learn from feedback underlies word learning difficulties in toddlers at risk for autism

Children’s assignment of novel words to nameless objects, over objects whose names they know (mutual exclusivity; ME) has been described as a driving force for vocabulary acquisition. Despite their ability to use ME to fast-map words (Preissler & Carey, 2005), children with autism show impaired language acquisition. We aimed to address this puzzle by building on studies showing that correct referent selection using ME does not lead to word learning unless ostensive feedback is provided on the child’s object choice (Horst & Samuelson, 2008). We found that although toddlers aged 2;0 at risk for autism can use ME to choose the correct referent of a word, they do not benefit from feedback for long-term retention of the word–object mapping. Further, their difficulty using feedback is associated with their smaller receptive vocabularies. We propose that difficulties learning from social feedback, not lexical principles, limits vocabulary building during development in children at risk for autism

Sediment Sorting and Rounding in a Basaltic Glacio-Fluvio-Aeolian Environment: hrisjkull Glacier, Iceland

Sediments and sedimentary rocks preserve a rich history of environment and climate. Identifying these signals requires an understanding of the physical and chemical processes that have affected sedimentary deposits [1]. Such processes include sorting and rounding during transport and chemical alteration through weathering and diagenesis. Although these processes have long been studied in quartz-dominated sedimentary systems [2], a lack of studies of basaltic sedimentary systems limits our interpretations of the environment and climate where mafic source rocks dominate, such as on Mars [3,4]. As part of the SAND-E: Semi-Autonomous Navigation for Detrital Environments project [5], which uses robotic operations to examine physical and chemical changes to sediments in basaltic glacio-fluvialaeolian environments, this research studies changes in sorting and rounding of fluvial-aeolian sediments along a glacier-proximal-to-glacier-distal transect in the outwash-plain of the risjkull glacier in SW Iceland (Fig. 1

Decorrelation Stretches (DCS) of Visible Images as a Tool for Sedimentary Provenance Investigations on Earth and Mars

The surface of Mars exhibits vast expanses of mafic sediments and ancient sedimentary rocks that record signals of climate and environment. To decipher the paleoenvironments, the sediment sources and transport histories must be con-strained, but it is not well known how physical fractionation and aqueous alteration affect mafic sediments during glacial, eolian, and fluvial processes. Semi-Autonomous Navigation for Detrital Environments (SAND-E), a NASA Planetary Science and Technology through Analog Research (PSTAR) project, bridges this gap through studies of sediment-grain properties and mineralogy in the glacio-XRD)-derived mineralogies

Clay Sediments from Basaltic Terrains: Implications for Sedimentary Processes on Mars

The Mars Science Laboratory (MSL) rover, Curiosity, has been traversing across fluvial, lacustrine, and eolian sedimentary rocks since it touched down in 2012. The CheMin X-ray diffractometer (XRD) on board Curiosity has revealed smectite clay minerals in most fluvio-lacustrine samples and abundant X-ray amorphous materials in all samples analyzed to date. For example, mudstones from the Sheepbed member at the base of the stratigraphic section and the lower part of the Murray formation contain on average ~7 to 20 wt% smectite and ~30 to 46 wt% X-ray amorphous abundances. On Earth, smectite and secondary X-ray amorphous materials are juvenile weathering products that are generated in sedimentary environments and ultimately record the interaction between primary igneous minerals and the hydrosphere, atmosphere, and biosphere. For this study, we investigated glacio-fluvio-eolian sediments generated in basaltic terrains as terrestrial analogs for the mudstones from Gale Crater, Mars. This work focuses on the clay sized sediments (<2 m) from these deposits as this grain size hosts the most mineralogically and geochemically altered detritus in sedimentary environments. The goal of investigating basaltic sedimentation is to create a terrestrial reference frame that sheds light on the paleoclimate and paleoaqueous conditions responsible for shaping the ancient sedimentary environments of Mars (e.g., Gale Crater and Jezero Crater)

Do acute elevations of serum creatinine in primary care engender an increased mortality risk?

Background: The significant impact Acute Kidney Injury (AKI) has on patient morbidity and mortality emphasizes the need for early recognition and effective treatment. AKI presenting to or occurring during hospitalisation has been widely studied but little is known about the incidence and outcomes of patients experiencing acute elevations in serum creatinine in the primary care setting where people are not subsequently admitted to hospital. The aim of this study was to define this incidence and explore its impact on mortality. Methods: The study cohort was identified by using hospital data bases over a six month period. Inclusion criteria: People with a serum creatinine request during the study period, 18 or over and not on renal replacement therapy. The patients were stratified by a rise in serum creatinine corresponding to the Acute Kidney Injury Network (AKIN) criteria for comparison purposes. Descriptive and survival data were then analysed. Ethical approval was granted from National Research Ethics Service (NRES) Committee South East Coast and from the National Information Governance Board. Results: The total study population was 61,432. 57,300 subjects with ‘no AKI’, mean age 64.The number (mean age) of acute serum creatinine rises overall were, ‘AKI 1’ 3,798 (72), ‘AKI 2’ 232 (73), and ‘AKI 3’ 102 (68) which equates to an overall incidence of 14,192 pmp/year (adult). Unadjusted 30 day survival was 99.9% in subjects with ‘no AKI’, compared to 98.6%, 90.1% and 82.3% in those with ‘AKI 1’, ‘AKI 2’ and ‘AKI 3’ respectively. After multivariable analysis adjusting for age, gender, baseline kidney function and co-morbidity the odds ratio of 30 day mortality was 5.3 (95% CI 3.6, 7.7), 36.8 (95% CI 21.6, 62.7) and 123 (95% CI 64.8, 235) respectively, compared to those without acute serum creatinine rises as defined. Conclusions: People who develop acute elevations of serum creatinine in primary care without being admitted to hospital have significantly worse outcomes than those with stable kidney function