Rational associahedra and noncrossing partitions

Each positive rational number x>0 can be written uniquely as x=a/(b-a) for coprime positive integers 0<a<b. We will identify x with the pair (a,b). In this paper we define for each positive rational x>0 a simplicial complex \Ass(x)=\Ass(a,b) called the {\sf rational associahedron}. It is a pure simplicial complex of dimension a-2, and its maximal faces are counted by the {\sf rational Catalan number} \Cat(x)=\Cat(a,b):=\frac{(a+b-1)!}{a!\,b!}. The cases (a,b)=(n,n+1) and (a,b)=(n,kn+1) recover the classical associahedron and its "Fuss-Catalan" generalization studied by Athanasiadis-Tzanaki and Fomin-Reading. We prove that \Ass(a,b) is shellable and give nice product formulas for its h-vector (the {\sf rational Narayana numbers}) and f-vector (the {\sf rational Kirkman numbers}). We define \Ass(a,b) via {\sf rational Dyck paths}: lattice paths from (0,0) to (b,a) staying above the line y = \frac{a}{b}x. We also use rational Dyck paths to define a rational generalization of noncrossing perfect matchings of [2n]. In the case (a,b) = (n, mn+1), our construction produces the noncrossing partitions of [(m+1)n] in which each block has size m+1.Comment: 21 pages, 8 figure

Pulsatile Hormonal Signaling to Extracellular Signal-Regulated Kinase: Exploring System Sensitivity to Gonadotropin-Releasing Hormone Pulse Frequency and Width

Gonadotropin-releasing hormone (GnRH) is secreted in brief pulses that stimulate synthesis and secretion of pituitary gonadotropin hormones and thereby mediate control of reproduction. It acts via G-protein-coupled receptors to stimulate effectors, including ERK. Information could be encoded in GnRH pulse frequency, width, amplitude, or other features of pulse shape, but the relative importance of these features is unknown. Here we examine this using automated fluorescence microscopy and mathematical modeling, focusing on ERK signaling. The simplest scenario is one in which the system is linear, and response dynamics are relatively fast (compared with the signal dynamics). In this case integrated system output (ERK activation or ERK-driven transcription) will be roughly proportional to integrated input, but we find that this is not the case. Notably, we find that relatively slow response kinetics lead to ERK activity beyond the GnRH pulse, and this reduces sensitivity to pulse width. More generally, we show that the slowing of response kinetics through the signaling cascade creates a system that is robust to pulse width. We, therefore, show how various levels of response kinetics synergize to dictate system sensitivity to different features of pulsatile hormone input. We reveal the mathematical and biochemical basis of a dynamic GnRH signaling system that is robust to changes in pulse amplitude and width but is sensitive to changes in receptor occupancy and frequency, precisely the features that are tightly regulated and exploited to exert physiological control in vivo

Outer zone electrons

Spatial and temporal behavior of high energy trapped electrons in outer zone of magnetospher

Accumulating exercise and postprandial health in adolescents

ArticleCopyright © 2015 Published by Elsevier Inc.Purpose: To examine the influence of exercise intensity on postprandial health outcomes in adolescents when exercise is accumulated throughout the day. Methods: 19 adolescents (9 male, 13.7 ± 0.4 y) completed three 1-day trials in a randomised order: 1) rest (CON); or four bouts of 2) 2 x 1 min cycling at 90% peak power with 75 s recovery (high-intensity interval exercise; HIIE); or 3) cycling at 90% of the gas exchange threshold (moderate-intensity exercise; MIE), which was work-matched to HIIE. Each bout was separated by 2 hours. Participants consumed a high fat milkshake for breakfast and lunch. Postprandial triacylglycerol (TAG), glucose, systolic blood pressure (SBP) and fat oxidation were assessed throughout the day. Results: There was no effect of trial on total area under the curve (TAUC) for TAG (P=0.87). TAUC-glucose was lower in HIIE compared to CON (P=0.03, ES=0.42) and MIE (P=0.04, ES=0.41), with no difference between MIE and CON (P=0.89, ES=0.04). Postprandial SBP was lower in HIIE compared to CON (P=0.04, ES=0.50) and MIE (P=0.04, ES=0.40), but not different between MIE and CON (P=0.52, ES=0.11). Resting fat oxidation was increased in HIIE compared to CON (P=0.01, ES=0.74) and MIE (P=0.05, ES=0.51), with no difference between MIE and CON (P=0.37, ES=0.24). Conclusion: Neither exercise trial attenuated postprandial lipaemia. However, accumulating brief bouts of HIIE, but not MIE, reduced postprandial plasma glucose and SBP, and increased resting fat oxidation in adolescent boys and girls. The intensity of accumulated exercise may therefore have important implications for health outcomes in youth.Sport and Health Sciences Research Committee, College of Life and Environmental Sciences, University of Exeter

Age- and Sex- Related Differences in Muscle Phosphocreatine and Oxygenation Kinetics during High Intensity Exercise in Adolescents and Adults

This is the author's post-print version of an article published in Nuclear Magnetic Resonance in Biomedicine, 2010, Vol. 23, Issue 6, pp. 569–577 Copyright © 2010 Wiley-Blackwell. The definitive version is available at www3.interscience.wiley.comThe aim of this investigation was to examine the adaptation of the muscle phosphates (e.g. phosphocreatine (PCr) and ADP) implicated in regulating oxidative phosphorylation, and oxygenation at the onset of high intensity exercise in children and adults. The hypotheses were threefold: primary PCr kinetics would be faster in children than adults; the amplitude of the PCr slow component would be attenuated in children; and the amplitude of the deoxyhaemoglobin/myoglobin (HHb) slow component would be reduced in children. Eleven children (5 girls, 6 boys, 13 ± 1 years) and 11 adults (5 women, 6 men, 24 ± 4 years) completed two to four constant work rate exercise tests within a 1.5 T MR scanner. Quadriceps muscle energetics during high intensity exercise were monitored using 31P-MRS. Muscle oxygenation was monitored using near-infrared spectroscopy. The time constant for the PCr response was not significantly different in boys (31 ± 10 s), girls (31 ± 10 s), men (44 ± 20 s) or women (29 ± 14 s, main effects: age, p = 0.37, sex, p = 0.25). The amplitude of the PCr slow component relative to end-exercise PCr was not significantly different between children (23 ± 23%) and adults (17 ± 13%, p = 0.47). End-exercise [PCr] was significantly lower, and [ADP] higher, in females (18 ± 4 mM and 53 ± 16 µM) than males (23 ± 4 mM, p = 0.02 and 37 ± 11 µM, p = 0.02), but did not differ with age ([PCr]: p = 0.96, [ADP]: p = 0.72). The mean response time for muscle tissue deoxygenation was significantly faster in children (22 ± 4 s) than adults (27 ± 7 s, p = 0.01). The results of this study show that the control of oxidative metabolism at the onset of high intensity exercise is adult-like in 13-year-old children, but that matching of oxygen delivery to extraction is more precise in adults

The mesospheric inversion layer and sprites

The vertical structure of temperature observed by SABER (Sounding of Atmosphere using Broadband Emission Radiometry) aboard TIMED (Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics) and sprites observations made during the Eurosprite 2003 to 2007 observational campaign were analyzed. Sprite observations were made at two locations in France, namely Puy de Dome in the French Massif Central and at the Pic du Midi in the French Pyrenees. It is observed that the vertical structure of temperature shows evidence for a Mesospheric Inversion Layer (MIL) on those days on which sprites were observed. A few events are also reported in which sprites were not recorded, although there is evidence of a MIL in the vertical structure of the temperature. It is proposed that breaking gravity waves produced by convective thunderstorms facilitate the production of (a) sprites by modulating the neutral air-density and (b) MILs via the deposition of energy. The same proposition has been used to explain observations of lightings as well as both MILs and lightning arising out of deep convections.Comment: 34 pages, 5figures. Accepted in Journal of Geophysical Research, US

Identification of phonological processes in preschool children's single-word productions

Speech and language therapists (SLTs) often refer to phonological data norms as part of their assessment protocols in evaluating the communication skills of the pre-school child. There is a variety of norms available and although broadly similar, differences are embedded within their definitions of mastery of the adult target system. Presence of velar fronting, stopping of affricates and [s] reduction in the dataset was found to mirror previous research. However, there was a lower than expected incidence by age groups of palato-alveolar fronting, stopping of fricatives and obstruent cluster reduction

New horizons in the understanding of the causes and management of diabetic foot disease: report from the 2017 Diabetes UK Annual Professional Conference Symposium

Diabetes-related foot disease remains a common problem. For wounds, classic teaching recommends the treatment of any infection, offloading the wound and ensuring a good blood supply, as well as ensuring that the other modifiable risk factors are addressed and optimized. There remain, however, several questions about these and other aspects of the care of diabetes-related foot disease. Some of these questions are addressed in the present report; in particular, the impact of newer technologies in the identification of any organisms present in a wound, as well as the use of novel approaches to treat infections. The use of new remote sensing technology to identify people at risk of developing foot ulceration is also considered, in an attempt to allow early intervention and prevention of foot ulcers. The psychological impact of foot disease is often overlooked, but with an increasing number of publications on the subject, the cause-and-effect role that psychology plays in foot disease, such as ulcers and Charcot neuroarthropathy, is considered. Finally, because of heterogeneity in diabetic foot studies, comparing results is difficult. A recently published document focusing on ensuring a standardized way of reporting foot disease trials is discussed

Understanding the diverse needs of subtitle users in a rapidly evolving media landscape

Audiences are increasingly using services, such as video on demand and the Web, to watch television programs. Broadcasters need to make subtitles available across all these new platforms. These platforms also create new design opportunities for subtitles along with the ability to customize them to an individual’s needs. To explore these new opportunities for subtitles, we have begun the process of reviewing the guidance for subtitles on television and evaluating the original user research. We have found that existing guidelines have been shaped by a mixture of technical constraints, industry practice, and user research, constrained by existing technical standards. This paper provides an overview of the subtitle research at BBC R&D over the past two years. Our research is revealing significant diversity in the needs and preferences of frequent subtitle users, and points to the need for personalization in the way subtitles are displayed. We are developing a new approach to the authoring and display of subtitles that can respond to the user requirements by adjusting the subtitle layout on the client device