Bethe Ansatz for a Quantum Supercoset Sigma Model

We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle density in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the lambda^{-1/2} effects and the 1/J effects. Our approach captures the first type, but not the second.Comment: 30 pages, 1 figure, v2: references adde

Solar Dynamics Observatory High Gain Antenna Handover Planning

The Solar Dynamics Observatory (SDO) is planned to launch in early 2009 as a mission to study the solar variability and its impact on Earth. To best satisfy its science goal, SDO will fly in a geosynchronous orbit with an inclination of approximately 29 deg. The spacecraft attitude is designed so that the science instruments point directly at the Sun with high accuracy. One of SDO's principal requirements is to obtain long periods of uninterrupted observations. The observations have an extremely high data volume so SDO must be in continuous contact with the ground during the observation periods. To maintain this contact, SDO is equipped with a pair of high gain antennas (HGAs) transmitting to a pair of ground antennas at the SDO ground station (SDOGS) located in White Sands, New Mexico. Either HGA can transmit to either SDOGS antenna. Neither HGA can be powered down. During a portion of each year, each of the HGA beams will intersect with the SDO body for a portion of the orbit. The original SDO antenna contact plan used each HGA for the half of each year during which its beam would not intersect the spacecraft. No data would be lost except, possibly, when switching from one antenna to another. After this plan was adopted, further analysis showed that daily handovers would be necessary for significant periods of the year. This unexpected need for extensive handovers necessitated that a handover design be developed to minimize the impact on the mission. This antenna handover design was developed and successfully tested with simulated data using the slew rate limits from preliminary jitter analysis. Subsequent analysis provided significant revision of allowed rates requiring modification of the handover plans

Factors That Influence Mathematical Creativity

Creativity is a psychological construct that has gained research popularity (Akgul & Kaveci, 2016), however it remains a challenging one to define. The variety of definitions promulgated to understand creativity hints at the complexity of the mental process. Furthermore, as a subset of creativity, domain-specific mathematical creativity has also garnered a variety of definitions. The transdisciplinary research on creativity (Sriraman & Haavold, 2017) is seminal in this world of fast-paced innovation, invention, solution, and synthesis. Considering every human being with at least average cognitive abilities possesses the ability to think creatively (Baran, 2011), developing students’ creative talents and abilities must be high on a list of educational priorities. Much of the literature surrounding mathematical creative thinking is centered on trying to quantify an individual’s creative thinking abilities. There have also been studies conducted that enabled researchers to describe various traits and demonstrate multiple levels of creativity. The basis of this work will be to synthesize the characteristics of mathematical creativity, analyze the impact of specific teaching approaches on mathematical creativity, and examine the relationship between student affect and mathematical creativity

Two chiral nonet model with massless quarks

We present a detailed study of a linear sigma model containing one chiral nonet transforming under U(1)$_A$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-anti diquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an "excited" pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.Comment: 22 pages, 8 figure

Toy model for two chiral nonets

Motivated by the possibility that nonets of scalar mesons might be described as mixtures of "two quark" and "four quark" components, we further study a toy model in which corresponding chiral nonets (containing also the pseudoscalar partners) interact with each other. Although the "two quark" and "four quark" chiral fields transform identically under SU(3)$_L \times$ SU(3)$_R$ transformations they transform differently under the U(1)$_A$ transformation which essentially counts total (quark + antiquark) content of the mesons. To implement this we formulate an effective Lagrangian which mocks up the U(1)$_A$ behavior of the underlying QCD. We derive generating equations which yield Ward identity type relations based only on the assumed symmetry structure. This is applied to the mass spectrum of the low lying pseudoscalars and scalars. as well as their "excitations". Assuming isotopic spin invariance, it is possible to disentangle the amount of"two quark" vs."four quark" content in the pseudoscalar $\pi, K ,\eta$ type states and in the scalar $\kappa$ type states. It is found that a small "four quark" content in the lightest pseudoscalars is consistent with a large "four quark" content in the lightest of the scalar $\kappa$ mesons. The present toy model also allows one to easily estimate the strength of a "four quark" vacuum condensate. There seems to be a rich and interesting structure.Comment: Numerical results updated, typos corrected, references update

Touchstone Stars: Highlights from the Cool Stars 18 Splinter Session

We present a summary of the splinter session on "touchstone stars" -- stars with directly measured parameters -- that was organized as part of the Cool Stars 18 conference. We discuss several methods to precisely determine cool star properties such as masses and radii from eclipsing binaries, and radii and effective temperatures from interferometry. We highlight recent results in identifying and measuring parameters for touchstone stars, and ongoing efforts to use touchstone stars to determine parameters for other stars. We conclude by comparing the results of touchstone stars with cool star models, noting some unusual patterns in the differences.Comment: Proceedings of the 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, Eds G. van Belle & H. Harri

Canonical Gravity, Diffeomorphisms and Objective Histories

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by constraints on the phase space so that a) The algebra of the generators reflects the algebra of the diffeomorphism group. b) The Poisson brackets of the basic fields with the generators reflects the space-time transformation properties of these basic fields. This suggests that in a purely Hamiltonian approach the requirement of diffeomorphism invariance should be interpreted to include b) and not just a) as one might naively suppose. Giving up b) amounts to giving up objective histories, even at the classical level. This observation has implications for Loop Quantum Gravity which are spelled out in a companion paper. We also describe an analogy between canonical gravity and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees' comments, accepted for publication in Classical and Quantum Gravit

Comparison of symptomatic and functional responses to vagus nerve stimulation in ANTHEM-HF, INOVATE-HF, and NECTAR-HF

AIMS: Clinical studies of vagal nerve stimulation (VNS) for heart failure with reduced ejection fraction have had mixed results to date. We sought to compare VNS delivery and associated changes in symptoms and function in autonomic regulation therapy via left or right cervical vagus nerve stimulation in patients with chronic heart failure (ANTHEM-HF), increase of vagal tone in heart failure (INOVATE-HF), and neural cardiac therapy for heart failure (NECTAR-HF) for hypothesis generation. METHODS AND RESULTS: Descriptive statistics were used to analyse data from the public domain for differences in proportions using Pearson\u27s chi-square test, differences in mean values using Student\u27s unpaired t-test, and differences in changes of mean values using two-sample t-tests. Guideline-directed medical therapy recommendations were similar across studies. Fewer patients were in New York Heart Association 3, and baseline heart rate (HR) was higher in ANTHEM-HF. In INOVATE-HF, VNS was aimed at peripheral neural targets, using closed-loop delivery that required synchronization of VNS to R-wave sensing by an intracardiac lead. Pulse frequency was low (1-2 Hz) because of a timing schedule allowing ≤3 pulses of VNS following at most 25% of detected R waves. NECTAR-HF and ANTHEM-HF used open-loop VNS delivery (i.e. independent of any external signal) aimed at both central and peripheral targets. In NECTAR-HF, VNS delivery at 20 Hz caused off-target effects that limited VNS up-titration in a majority of patients. In ANTHEM-HF, VNS delivery at 10 Hz allowed up-titration until changes in HR dynamics were confirmed. Six months after VNS titration, significant improvements in both HR and HR variability occurred only in ANTHEM-HF. When ANTHEM-HF and NECTAR-HF were compared, greater improvements from baseline were observed in ANTHEM-HF in standard deviation in normal-to-normal R-R intervals (94 ± 26 to 111 ± 50 vs. 146 ± 48 to 130 ± 52 ms; P \u3c 0.001), left ventricular ejection fraction (32 ± 7 to 37 ± 0.4 vs. 31 ± 6 to 33 ± 6; P \u3c 0.05), and Minnesota Living with Heart Failure mean score (40 ± 14 to 21 ± 10 vs. 44 ± 22 to 36 ± 21; P \u3c 0.002). When compared with INOVATE-HF, greater improvement in 6-min walk distance was observed in ANTHEM-HF (287 ± 66 to 346 ± 78 vs. 304 ± 111 to 334 ± 111 m; P \u3c 0.04). CONCLUSIONS: In this post-hoc analysis, differences in patient demographics were seen and may have caused the differential responses in symptoms and function observed in association with VNS. Major differences in technology platforms, neural targets, VNS delivery, and HR and HR variability responses could have also potentially played a very important role. Further study is underway in a randomized controlled trial with these considerations in mind

A novel approach to model cumulative stress:Area under the s-factor curve

OBJECTIVE: Using a large longitudinal sample of adults from the Midlife in the United States (MIDUS) study, the present study extended a recently developed hierarchical model to determine how best to model the accumulation of stressors, and to determine whether the rate of change in stressors or traditional composite scores of stressors are stronger predictors of health outcomes.METHOD: We used factor analysis to estimate a stress-factor score and then, to operationalize the accumulation of stressors we examined five approaches to aggregating information about repeated exposures to multiple stressors. The predictive validity of these approaches was then assessed in relation to different health outcomes.RESULTS: The prediction of chronic conditions, body mass index, difficulty with activities of daily living, executive function, and episodic memory later in life was strongest when the accumulation of stressors was modeled using total area under the curve (AUC) of estimated factor scores, compared to composite scores that have traditionally been used in studies of cumulative stress, as well as linear rates of change.CONCLUSIONS: Like endogenous, biological markers of stress reactivity, AUC for individual trajectories of self-reported stressors shows promise as a data reduction technique to model the accumulation of stressors in longitudinal studies. Overall, our results indicate that considering different quantitative models is critical to understanding the sequelae and predictive power of psychosocial stressors from midlife to late adulthood.</p